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arXiv · 1302.2381

On higher congruences between automorphic forms

Tobias Berger·Krzysztof Klosin·Kenneth Kramer
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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 π_0 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 π_0 and other automorphic forms. We apply this result to several situations including the congruences described by Mazur's Eisenstein ideal.

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Tobias Berger, Krzysztof Klosin, Kenneth Kramer. 2013-02-11. On higher congruences between automorphic forms. https://arxiv.org/abs/1302.2381

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