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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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 PDF
Math. Comp. 74 (2005), 1545-1557 Request permission


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
  • MR Author ID: 759256
  • Email:
  • Fernando Rodriguez Villegas
  • Affiliation: Department of Mathematics, University of Texas at Austin, Texas 78712
  • MR Author ID: 241496
  • Email:
  • B. Gross
  • Affiliation: Department of Mathematics, Harvard University, Cambridge, Massacusetts 02138
  • MR Author ID: 77400
  • Email:
  • 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:
  • MathSciNet review: 2137017