On the modularity level of modular abelian varieties over number fields
Number Theory
2014-11-14 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1002.0492,
title = {On the modularity level of modular abelian varieties over number fields},
author = {Enrique Gonzalez-Jimenez and Xavier Guitart},
journal= {arXiv preprint arXiv:1002.0492},
year = {2014}
}