Computing Congruences of Modular Forms and Galois Representations Modulo Prime Powers

Details Computing Congruences of Modular Forms and Galois Representations Modulo Prime Powers Computing Congruences of Modular Forms and Galois Representations Modulo Prime Powers

2009-09-15

arxiv.org/abs/0909.2724v2

Mathematics

Number Theory

26 pages

Scientific paper

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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