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Computing congruences of modular forms and Galois representations modulo prime powers

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  • Xavier Taixés

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  • Gabor Wiese
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    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.

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    File URL: http://www.econ.upf.edu/docs/papers/downloads/1248.pdf
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    Bibliographic Info

    Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 1248.

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    Date of creation: Jan 2010
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    Handle: RePEc:upf:upfgen:1248

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    Web page: http://www.econ.upf.edu/

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