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Computing weight $2$ modular forms of level $p^2$

Authors: Ariel Pacetti and Fernando Rodriguez Villegas; with an appendix by B. Gross
Journal: Math. Comp. 74 (2005), 1545-1557
MSC (2000): Primary 11F11; Secondary 11E20, 11Y99
Published electronically: September 10, 2004
MathSciNet review: 2137017
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Abstract: For a prime $p$ we describe an algorithm for computing the Brandt matrices giving the action of the Hecke operators on the space $V$ of modular forms of weight $2$ and level $p^2$. For $p \equiv 3 \bmod 4$ we define a special Hecke stable subspace $V_0$ of $V$ which contains the space of modular forms with CM by the ring of integers of $\mathbb Q(\sqrt{-p})$ and we describe the calculation of the corresponding Brandt matrices.

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Additional Information

Ariel Pacetti
Affiliation: Department of Mathematics, University of Texas at Austin, Texas 78712

Fernando Rodriguez Villegas
Affiliation: Department of Mathematics, University of Texas at Austin, Texas 78712

B. Gross
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massacusetts 02138

Received by editor(s): February 18, 2003
Received by editor(s) in revised form: December 16, 2003
Published electronically: September 10, 2004
Additional Notes: The first and second authors were supported in part by grants from TARP and NSF (DMS-99-70109); they would like to thank the Department of Mathematics at Harvard University, where part of this work was done, for its hospitality
Article copyright: © Copyright 2004 American Mathematical Society