The Jacquet-Langlands correspondence, Eisenstein congruences, and integral L-values in weight 2

Abstract

We use the Jacquet-Langlands correspondence to generalize well-known congruence results of Mazur on Fourier coefficients and L-values of elliptic modular forms for prime level in weight 2 both to nonsquare level and to Hilbert modular forms.

arXiv comment16 pages; this is a corrected and annotated version to the published version--the main correction is the addition of hypotheses in Theorem 2.1 in the case of base field with class number > 1; all the results stated in the introduction are unchanged