On the modularity level of modular abelian varieties over number fields

Details On the modularity level of modular abelian varieties over number fields On the modularity level of modular abelian varieties over number fields

2010-02-02

arxiv.org/abs/1002.0492v1

J. Number Theory 130, no. 7, 1560-1570 (2010)

Mathematics

Number Theory

Scientific paper

10.1016/j.jnt.2010.03.003

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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