  Previous works have shown that certain weight $2$ newforms are $p$-adic
limits of weakly holomorphic modular forms under repeated application of the
$U$-operator. The proofs of these theorems originally relied on the theory of
harmonic Maass forms. Ahlgren and Samart obtained strengthened versions of
these results using the theory of holomorphic modular forms. Here, we use such
techniques to express all weight $2$ CM newforms which are eta quotients as
$p$-adic limits. In particular, we show that these forms are $p$-adic limits of
the derivatives of the Weierstrass mock modular forms associated to their
elliptic curves.
