Question: The Fairly OddParents included  crossover episodes that premiered between which years?

Context paragraphs:
The Fairly OddParents (season 3): The Fairly OddParents' third season began on January 20, 2003. " The Fairly OddParents" first movie, "Abra-Catastrophe!"  aired in the summer of 2003.

The Fairly OddParents (season 5): The 5th season of "The Fairly OddParents" started on  14, 2005 (2005--) .  In this season, the show aired its seventh TV movie, "Fairy Idol", and three "The Jimmy Timmy Power Hour" movies.  After "The Jerkinators", "The Fairly OddParents" and "" seem to end, but later in 2006, they aired episodes that chronologically come before the season finale.  After November 25, 2006, "Jimmy Neutron" ended its run, and "The Fairly OddParents" was sent on hiatus for 15 months, between December 2006 and December 2007.

The Fairly OddParents: Shadow Showdown: The Fairly OddParents: Shadow Showdown is a platforming video game released in 2004 for Microsoft Windows, GameCube, PlayStation 2, and Game Boy Advance by THQ.  ImaginEngine developed the PC version while Blitz Games developed the GameCube and PlayStation 2 versions.  The game is based on the animated series "The Fairly OddParents" and is the sequel to "".

The Fairly OddParents: Breakin' da Rules: The Fairly OddParents: Breakin' Da Rules is a video game released for the Game Boy Advance, Nintendo GameCube, PlayStation 2, Xbox, and the PC in North America in 2003.  It is based on the Nickelodeon cartoon "The Fairly OddParents".  It was developed by Blitz Games and published by THQ.  Its sequel, "" was released on the GameCube, Game Boy Advance and PlayStation 2.  The console versions of this game feature a different plot than the PC version.  It is the only video game based on "The Fairly OddParents" to be released for Xbox.

Butch Hartman: Elmer Earl Hartman IV, better known as Butch Hartman (born January 10, 1965), is an American animator, writer, director, producer, and actor, best known for creating the Nickelodeon cartoons "The Fairly OddParents", "Danny Phantom", "T.U.F.F. Puppy" and "Bunsen Is a Beast".  Hartman also owns a production company, Billionfold, Inc., which he uses primarily to produce his shows.  Hartman has been an executive producer on "Fairly OddParents" since its series debut in 2001.

List of The Fairly OddParents episodes: "The Fairly OddParents" is an animated American television series that airs on Nicktoons, and previously Nickelodeon.  The series is based on a series of "Oh Yeah!  Cartoons", beginning with the short "The Fairly OddParents!" .

The Fairly OddParents (film series): The Fairly OddParents is a series of live action spinoff telefilms produced through Nickelodeon, loosely based on Butch Hartman's animated series "The Fairly OddParents".  The series currently comprises three films: "" (2011), "A Fairly Odd Christmas" (2012), and "A Fairly Odd Summer" (2014).  The three films take place in a separate universe from the animated series.

Steve Marmel: Steve Marmel (born December 17, 1964) is an American television writer and producer who has worked on many animated TV series, including "The Fairly OddParents", "I Am Weasel", "Danny Phantom", "Family Guy" and "Yin Yang Yo! ".  During his work on "The Fairly OddParents" he frequently co-wrote episodes with Butch Hartman.  Marmel also created the series "Sonny with a Chance" as well as the series "Mech-X4".

The Fairly OddParents (season 4): "The Fairly OddParents" fourth season began on February 16, 2004.  The second movie, "Channel Chasers" aired in the summer of 2004, and for the 4th time, 2 Nicktoons make crossovers in "The Jimmy Timmy Power Hour".  The season officially ended with "Genie Meanie Minie Mo".

The Jimmy Timmy Power Hour: The Jimmy Timmy Power Hour is a television crossover film trilogy set between the universes of "" and "The Fairly OddParents".  The film series consists of the following: a first film of the same name as this series, a second titled "The Jimmy Timmy Power Hour II: When Nerds Collide!"  and a third, "The Jimmy Timmy Power Hour III: The Jerkinators!"  The films premiered on Nickelodeon between 2004 and 2006, and were subsequently released to home video.  The specials combines 2D animation and CGI graphics.

Supporting paragraphs: The Fairly OddParents (season 4) The Jimmy Timmy Power Hour
Answer: 2004 and 2006