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

Author(s): Ariel Pacetti; Fernando Rodriguez Villegas; with an appendix by B. Gross.
Journal: Math. Comp. 74 (2005), 1545-1557.
MSC (2000): Primary 11F11; Secondary 11E20, 11Y99
Posted: September 10, 2004
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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
Email: apacetti@math.utexas.edu

Fernando Rodriguez Villegas
Affiliation: Department of Mathematics, University of Texas at Austin, Texas 78712
Email: villegas@math.utexas.edu

B. Gross
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massacusetts 02138
Email: gross@math.harvard.edu

DOI: 10.1090/S0025-5718-04-01709-0
PII: S 0025-5718(04)01709-0
Received by editor(s): February 18, 2003
Received by editor(s) in revised form: December 16, 2003
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society

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