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ISSN 1088-6826(e) ISSN 0002-9939(p)

The image and kernel of Atkin's $U_{p}$ operator modulo

Author: Michael Dewar
Journal: Proc. Amer. Math. Soc. 140 (2012), 1931-1938
MSC (2010): Primary 11F11, 11F33
Posted: October 14, 2011
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Abstract: We compute the image of Atkin's $U_{p}$ operator on reduced modular forms. If $A\geq 1$ and $2\leq B \leq p+1$ , then $U_{p}: \widetilde M_{Ap+B}\left ( \Gamma _{1}(N) \right ) \onto \widetilde M_{A+B} \left (\Gamma _{1}(N) \right )$ is a surjection. In particular, the dimension of $\ker U_{p}$ is known for weights at least .

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