Congruences for modular forms mod 2 and quaternionic -ideal classes
arXiv:1701.07864
Abstract
We prove many simultaneous congruences mod 2 for elliptic and Hilbert modular forms among forms with different Atkin--Lehner eigenvalues. The proofs involve the notion of quaternionic -ideal classes and the distribution of Atkin--Lehner signs among newforms.
arXiv comment19 pages; minor revisions, to appear in Canad. J. Math