LMS Journal of Computation and Mathematics

Table of Contents - Volume 14 - 2011  

Research Article

Computations with classical and p-adic modular forms

Alan G. B. Laudera1

a1 Mathematical Institute, 24-29 St Giles, Oxford, United Kingdom (email: lauder@maths.ox.ac.uk)

Abstract

We present p-adic algorithms for computing Hecke polynomials and Hecke eigenforms associated to spaces of classical modular forms, using the theory of overconvergent modular forms. The algorithms have a running time which grows linearly with the logarithm of the weight and are well suited to investigating the dimension variation of certain p-adically defined spaces of classical modular forms.

(Received March 18 2011)

(Online publication August 2011)

2000 Mathematics Subject Classification

  • 11G18 (primary);
  • 11Y16;
  • 11-04 (secondary)

Footnotes

The author is a Royal Society University Research Fellow. His work is supported in part by a grant from the European Research Council (204083).

Dedicated to Daqing Wan