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

@article{Ventosa2009ComputingCO,
title={Computing Congruences of Modular Forms and Galois Representations Modulo Prime Powers},
author={Xavier Taixes i Ventosa and Gabor Wiese},
journal={Contemporary mathematics},
year={2009},
volume={521},
pages={145-170}
}
• Published 15 September 2009
• Mathematics
• Contemporary mathematics
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…

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