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

  • Kimball Martin,
    Department of Mathematics, University of Oklahoma
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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 $S$-ideal classes and the distribution of Atkin--Lehner signs among newforms.
Keywords: modular forms, congruences, quaternion algebras modular forms, congruences, quaternion algebras
MSC Classifications: 11F33, 11R52 show english descriptions Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
Quaternion and other division algebras: arithmetic, zeta functions
11F33 - Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]
11R52 - Quaternion and other division algebras: arithmetic, zeta functions
 

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