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arXiv · 1002.0492

On the modularity level of modular abelian varieties over number fields

Enrique Gonzalez-Jimenez·Xavier Guitart
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Abstract

Let f be a weight two newform for Gamma_1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety A_f over certain number fields L. The strategy we follow is to compute the restriction of scalars Res_{L/\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 N_L(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 N_L(B) belongs to Z and N_L(B)*f_L^{dim B}=N^{dim B}, where f_L is the conductor of L.

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Enrique Gonzalez-Jimenez, Xavier Guitart. 2010-02-02. On the modularity level of modular abelian varieties over number fields. https://doi.org/10.1016/j.jnt.2010.03.003

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