Mathematical Research Letters
Volume 21 (2014)
On higher congruences between automorphic forms
Pages: 71 – 82
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 $\pi_0$, 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 $\pi_0$ and other automorphic forms. We apply this result to several situations including the congruences described by Mazur’s Eisenstein ideal.
congruences, automorphic forms
2010 Mathematics Subject Classification