Congruences for modular forms mod 2 and quaternionic $S$ -ideal classes

preprint2017arXivOpen access

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 $S$ -ideal classes and the distribution of Atkin--Lehner signs among newforms.

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Congruences for modular forms mod 2 and quaternionic $S$ -ideal classes

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Congruences for modular forms mod 2 and quaternionic SSS-ideal classes

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Congruences for modular forms mod 2 and quaternionic $S$ -ideal classes