Computing Congruences of Modular Forms and Galois Representations Modulo\n Prime Powers

2009/09/15 by Xavier Taixés i Ventosa, Ventosa, Xavier Taixes i, Gabor Wiese +1 · 2 citations
Mathematics · #11F11 #11F33 (primary) #11F80 #11Y40. #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0909.2724

openalex publication_date 2009/09/15 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

This article starts a computational study of congruences of modular forms and\nmodular Galois representations modulo prime powers. Algorithms are described\nthat compute the maximum integer modulo which two monic coprime integral\npolynomials have a root in common in a sense that is defined. These techniques\nare applied to the study of congruences of modular forms and modular Galois\nrepresentations modulo prime powers. Finally, some computational results with\nimplications on the (non-)liftability of modular forms modulo prime powers and\npossible generalisations of level raising are presented.\n

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