On the modularity level of modular abelian varieties over number fields |
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Authors: | Enrique Gonzá lez-Jimé nez,Xavier Guitart |
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Affiliation: | a Universidad Autónoma de Madrid, Departamento de Matemáticas and Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Madrid, Spain b Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3 (Edifici Omega), 08034, Barcelona, Spain |
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Abstract: | Let f be a weight two newform for Γ1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety Af over certain number fields L. The strategy we follow is to compute the restriction of scalars ResL/Q(B), and then to apply Milne's formula for the conductor of the restriction of scalars. In this way we obtain an expression for the local exponents of the conductor NL(B). Under some hypothesis it is possible to give global formulas relating this conductor with N. For instance, if N is squarefree, we find that NL(B) belongs to Z and , where fL is the conductor of L. |
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Keywords: | Modular abelian varieties Conductors |
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