<PAGE>

                                                                   EXHIBIT 4.03

     THIS WARRANT AND THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE
     NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933. THEY MAY NOT BE
     SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED, OR OTHERWISE TRANSFERRED
     EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE
     SECURITIES ACT OF 1933, OR AN OPINION OF COUNSEL SATISFACTORY TO THE
     COMPANY THAT REGISTRATION IS NOT REQUIRED UNDER SUCH ACT OR UNLESS SOLD
     PURSUANT TO RULE 144 UNDER SUCH ACT.

                                                                     Void after
                                                              November 18, 2003

                            STOCK PURCHASE WARRANT
                            ----------------------

     This Warrant is issued to ____________________________ by dsl.net, inc., a
Delaware corporation (the "Company"), pursuant to the terms of that certain Note
and Warrant Purchase Agreement (the "Purchase Agreement") dated as of November
18, 1998, in connection with the Company's issuance to the holder of this
Warrant of a Convertible Promissory Note dated as of November 18, 1998 (the
"Note"), for the principal amount of One Hundred and Twenty-Five Thousand
Dollars ($125,000).

1.   Purchase of Shares.  Subject to the terms and conditions hereinafter set
     ------------------
forth and set forth in the Agreement, the holder of this Warrant is entitled,
upon surrender of this Warrant at the principal office of the Company (or at
such other place as the Company shall notify the holder hereof in writing), to
purchase from the Company up to that number of fully paid and nonassessable
shares of preferred stock or equity securities of the Company, as more fully
described below (the "Preferred Stock"), that equals the quotient obtained by
dividing (a) Thirty-One Thousand Two Hundred and Fifty (31,250), by (b) the
price per share of equity securities sold to investors in the Company's next
transaction or series of related transactions in which the Company sells equity
securities and in which the gross proceeds to the Company equal or exceed One
Million Dollars ($1,000,000) (excluding the aggregate amount of debt securities
converted into equity securities upon conversion of this Note and other notes
outstanding as of the date hereof) (the "Next Equity Financing").  The Company
currently has shares of Series A Preferred Stock authorized; however, the
Company currently anticipates that such series of Preferred Stock will be
converted into shares of Common Stock prior to the Next Equity Financing.  After
giving effect to such conversion, the Company currently anticipates that the
securities issuable to investors in the Next Equity Financing will be shares of
a newly authorized series of Preferred Stock to be designated Series A Preferred
Stock.  Except as otherwise provided above, the class of capital stock or series
of Preferred Stock issuable upon exercise of this Warrant shall be the same
class or series as shall be issued in the Next Equity Financing.  Accordingly,
if the Company issues Series A Preferred Stock to the investors in the Next
Equity Financing, this Warrant shall be exercisable for shares of the Company's
Series A Preferred Stock.  Conversely, if the Company issues another series of
Preferred Stock or another class of capital stock to the investors in the Next
Equity Financing, this Warrant shall be exercisable for such other series of
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                                      -2-


the Company's Preferred Stock or such other class of the Company's capital
stock, as the case may be. The shares of Preferred Stock issuable pursuant to
this Section 1 (the "Shares") shall also be subject to adjustment pursuant to
Section 8 hereof. If the securities issuable to investors in the Next Equity
Financing are not Preferred Stock, all references in this Warrant to "Preferred
Stock" shall be deemed to be adjusted accordingly.

2.   Purchase Price.  The purchase price for the Shares shall be the price per
     --------------
share of equity securities sold to investors in the Company's Next Equity
Financing.  Such price shall be subject to adjustment pursuant to Section 8
hereof (such price, as adjusted from time to time, is herein referred to as the
"Exercise Price").

3.   Exercise Period.  This Warrant shall become exercisable upon the closing of
     ---------------
the Next Equity Financing and it shall remain so exercisable until and including
November 18, 2003.

4.   Method of Exercise.  While this Warrant remains outstanding and exercisable
     ------------------
in accordance with Section 3 above, the holder may exercise, in whole or in
part, the purchase rights evidenced hereby.  Such exercise shall be effected by:

          (i)    the surrender of the Warrant, together with a duly executed
     copy of the form of subscription attached hereto, to the Secretary of the
     Company at its principal offices; and

          (ii)   the payment to the Company of an amount equal to the aggregate
     Exercise Price for the number of Shares being purchased.

5.   Net Exercise.  In lieu of cash exercising this Warrant, the holder of this
     ------------
Warrant may elect to receive shares equal to the value of this Warrant (or the
portion thereof being canceled) by surrender of this Warrant at the principal
office of the Company together with notice of such election, in which event the
Company shall issue to the holder hereof a number of shares of Preferred Stock
computed using the following formula:

                         Y (A-B)
                         -------
                    X=      A
Where

     X --      The number of shares of Preferred Stock to be issued to the
               holder of this Warrant.
     Y --      The number of shares of Preferred Stock purchasable under
               this Warrant.
     A --      The fair market value of one share of the Company's
               Preferred Stock.
     B --      The Exercise Price (as adjusted to the date of such
               calculations).

For purposes of this Paragraph 5, the fair market value of Preferred Stock shall
mean the average of the closing bid and asked prices of the Preferred Stock
quoted in the over-the-counter market in which the Preferred Stock is traded, or
the closing price quoted on any exchange on which the Preferred Stock is listed,
whichever is applicable, as published in the New York Edition of The Wall Street
                                                                 --- -----------
Journal for the ten (10) trading days prior to the date of determination of fair
-------
market
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                                      -3-

value (or such shorter period of time during which such stock was traded over-
the-counter or on such exchange). If the Preferred Stock is not traded on the
over-the-counter market or on an exchange, the fair market value shall be the
price per share that the Company could obtain from a willing buyer for shares of
Preferred Stock sold by the Company from authorized but unissued shares, as such
prices shall be determined in good faith by the Company's Board of Directors.

6.   Certificates for Shares.  Upon the exercise of the purchase rights
     -----------------------
evidenced by this Warrant, one or more certificates for the number of Shares so
purchased shall be issued as soon as practicable thereafter, and in any event
within thirty (30) days of the delivery of the subscription notice.

7.   Issuance of Shares.  The Company covenants that the Shares, when issued
     ------------------
pursuant to the exercise of this Warrant, will be duly and validly issued, fully
paid and nonassessable and free from all taxes, liens, and changes with respect
to the issuance thereof.

8.   Adjustment of Exercise Price and Number of Shares.  The number of and kind
     -------------------------------------------------
of securities purchasable upon exercise of this Warrant and the Exercise Price
shall be subject to adjustment from time to time as follows:

          (a)  Subdivisions, Combinations and Other Issuances.  If the Company
               ----------------------------------------------
     shall at any time prior to the expiration of this Warrant subdivide its
     Preferred Stock, by split-up or otherwise, or combine its Preferred Stock,
     or issue additional shares of its Preferred Stock or Common Stock as a
     dividend with respect to any shares of its Preferred Stock, the number of
     Shares issuable on the exercise of this Warrant shall forthwith be
     proportionately increased in the case of a subdivision or stock dividend,
     or proportionately decreased in the case of a combination. Appropriate
     adjustments shall also be made to the purchase price payable per share, but
     the aggregate purchase price payable for the total number of Shares
     purchasable under this Warrant (as adjusted) shall remain the same. Any
     adjustment under this Section 8(a) shall become effective at the close of
     business on the date the subdivision or combination becomes effective, or
     as of the record date of such dividend, or in the event that no record date
     is fixed, upon the making of such dividend.

          (b)  Reclassification, Reorganization and Consolidation.  In case of
               --------------------------------------------------
     any reclassification, capital reorganization, or change in the Preferred
     Stock of the Company (other than as a result of a subdivision, combination,
     or stock dividend provided for in Section 8(a) above), then. as a condition
     of such reclassification, reorganization, or change, lawful provision shall
     be made, and duly executed documents evidencing the same from the Company
     or its successor shall be delivered to the holder of this Warrant, so that
     the holder of this Warrant shall have the right at any time prior to the
     expiration of this Warrant to purchase, at a total price equal to that
     payable upon the exercise of this Warrant, the kind and amount of shares of
     stock and other securities and property receivable in connection with such
     reclassification, reorganization, or change by a holder of the same number
     of shares of Preferred Stock as were purchasable by the holder of this
     Warrant immediately prior to such reclassification, reorganization, or
     change. In any such case appropriate provisions shall be made with respect
     to the rights and interest of the holder of this Warrant so that the
     provisions hereof shall thereafter be applicable with respect to any shares
     of stock or other securities and property deliverable upon exercise hereof,
     and appropriate adjustments shall be made to the purchase price per share
     payable hereunder, provided the aggregate price shall remain the same.
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                                      -4-

          (c)  Notice of Adjustment. When any adjustment is required to be
               --------------------
     made in the number or kind of shares purchasable upon exercise of the
     Warrant, or in the Exercise Price, the Company shall promptly notify the
     holder of such event and of the number of shares of Preferred Stock or
     other securities or property thereafter purchasable upon exercise of this
     Warrant.

9.   Fractional Shares or Scrip.  No fractional shares or scrip representing
     --------------------------
fractional shares shall be issued upon the exercise of this Warrant, but in lieu
of such fractional shares the Company shall make a cash payment therefor on the
basis of the Exercise Price then in effect.

10.  No Stockholder Rights.  Prior to exercise of this Warrant, the holder
     ---------------------
shall not be entitled to any rights of a stockholder with respect to the Shares,
including (without limitation) the right to vote such Shares, receive dividends
or other distributions thereon, exercise preemptive rights or be notified of
stockholder meetings, and such holder shall not be entitled to any notice or
other communication concerning the business or affairs of the Company.

11.  Successors and Assigns.  The terms and provisions of this Warrant and the
     ----------------------
Purchase Agreement shall inure to the benefit of, and be binding upon, the
Company and the holders hereof and their respective successors and assigns.

12.  Amendments and Waivers.  Any term of this Warrant may be amended and the
     ----------------------
observance of any terms of this Warrant may be waived (either generally or in a
particular instance and either retroactively or prospectively), with the written
consent of the Company and the holder.
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                                      -5-

14.  Governing Law.  This Warrant shall be governed by the laws of the State of
     -------------
California as applied to agreements among California residents made and to be
performed entirely within the State of California.

                                        dsl.net, inc.


                                        By: /s/ John M. Jaser
                                            -----------------

                                        Title: President
                                               ---------

                                        Address:  50 Washington Street
                                                  Norwalk, CT 06854