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

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- by Ariel Pacetti and Fernando Rodriguez Villegas; with an appendix by B. Gross
- Math. Comp.
**74**(2005), 1545-1557 - DOI: https://doi.org/10.1090/S0025-5718-04-01709-0
- Published electronically: 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.## References

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## Bibliographic Information

**Ariel Pacetti**- Affiliation: Department of Mathematics, University of Texas at Austin, Texas 78712
- MR Author ID: 759256
- Email: apacetti@math.utexas.edu
**Fernando Rodriguez Villegas**- Affiliation: Department of Mathematics, University of Texas at Austin, Texas 78712
- MR Author ID: 241496
- Email: villegas@math.utexas.edu
**B. Gross**- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massacusetts 02138
- MR Author ID: 77400
- Email: gross@math.harvard.edu
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp.
**74**(2005), 1545-1557 - MSC (2000): Primary 11F11; Secondary 11E20, 11Y99
- DOI: https://doi.org/10.1090/S0025-5718-04-01709-0
- MathSciNet review: 2137017