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Computing congruences of modular forms and Galois representations modulo prime powers

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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.

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  • Xavier Taixés & Gabor Wiese, 2010. "Computing congruences of modular forms and Galois representations modulo prime powers," Economics Working Papers 1248, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:1248
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