  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.
