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Computing congruences of modular forms and Galois representations modulo prime powers
Taixés, Xavier; Wiese, Gabor
Universitat Pompeu Fabra. Departament d'Economia i Empresa
This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.
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