Berger, Tobias; Klosin, Krzysztof; Kramer, Kenneth On higher congruences between automorphic forms. (English) Zbl 1367.11050 Math. Res. Lett. 21, No. 1, 71-82 (2014). Summary: 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. Cited in 5 Documents MSC: 11F33 Congruences for modular and \(p\)-adic modular forms Keywords:congruences; automorphic forms PDFBibTeX XMLCite \textit{T. Berger} et al., Math. Res. Lett. 21, No. 1, 71--82 (2014; Zbl 1367.11050) Full Text: DOI arXiv