On Higher Congruences between Automorphic Forms

Abstract

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform π0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of π0 and other automorphic forms. We apply this result to several situations including the congruences described by Mazur’s Eisenstein ideal.

Cite this paper

@inproceedings{Berger2013OnHC, title={On Higher Congruences between Automorphic Forms}, author={Tobias Berger and Kenneth Kramer}, year={2013} }