congruences for modular forms
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2018 ◽  
Vol 70 (5) ◽  
pp. 1076-1095 ◽  
Author(s):  
Kimball Martin

AbstractWe 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 quaternionicS-ideal classes and the distribution of Atkin–Lehner signs among newforms.


2008 ◽  
Vol 04 (01) ◽  
pp. 1-13 ◽  
Author(s):  
YAIM COOPER ◽  
NICHOLAS WAGE ◽  
IRENA WANG

In this paper, we consider modular forms f(z) whose q-series expansions ∑b(n)qn have coefficients in a localized ring of algebraic integers [Formula: see text]. Extending results of Serre and Ono, we show that if f has non-positive weight, a congruence of the form b(ℓn + a) ≡ 0 (mod ν), where ν is a place over ℓ in [Formula: see text], can hold for only finitely many primes ℓ ≥ 5. To obtain this, we establish an effective bound on ℓ in terms of the weight and the structure of f(z).


2007 ◽  
Vol 126 (2) ◽  
pp. 193-199 ◽  
Author(s):  
Scott Ahlgren ◽  
Mugurel Barcau

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