Paper #1248

Title:

Computing congruences of modular forms and Galois representations modulo prime powers

Authors:

Xavier Taixés and Gabor Wiese

Date:

January 2010

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.

JEL codes:

11F33 (primary); 11F11, 11F80, 11Y40.

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