Computing congruences of modular forms and Galois representations modulo prime powers

Xavier Taixés i Ventosa, Gabor Wiese

Type: Other

Publication Date: 2010-01-01

Citations: 11

DOI: https://doi.org/10.1090/conm/521/10279

Abstract

This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers.Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials have a root in common in a sense that is defined.These techniques are applied to the study of congruences of modular forms and modular Galois representations modulo prime powers.Finally, some computational results with implications on the (non-)liftability of modular forms modulo prime powers and possible generalisations of level raising are presented.

Locations

Contemporary mathematics - American Mathematical Society - View
arXiv (Cornell University) - View - PDF
RePEc: Research Papers in Economics - View - PDF
Repositori digital de la UPF (Universitat Pompeu Fabra) - View - PDF
LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) - View - PDF

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+ PDF Chat	On higher congruences between automorphic forms	2014	Tobias Berger Krzysztof Klosin Kenneth Kramer
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+ PDF Chat	Examples of abelian surfaces failing the local–global principle for isogenies	2021	Barinder S. Banwait
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Works Cited by This (13)

Action	Title	Year	Authors
+	Theoretical and algorithmic aspects of congruences between modular Galois representations	2010	Xavier Taixés i Ventosa
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+	On the congruence of modular forms	1987	Jacob Sturm
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust
+	ON MODULAR SYMBOLS AND THE COHOMOLOGY OF HECKE TRIANGLE SURFACES	2009	Gabor Wiese
+ PDF Chat	Modular curves and the eisenstein ideal	1977	Barry Mazur
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+	Galois representations attached to elliptic curves and diophantine problems	2013	Gerhard Frey