Computations with classical and p-adic modular forms

Abstract

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.