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On the modularity level of modular abelian varieties over number fields

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10.1016/j.jnt.2010.03.003
 
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Gonzalez Jimenez, Enrique
Guitart Morales, Xavier
Document typeArticle
Defense date2010-07
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
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 A f 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 NL (B)f dim B L = N dim B, where fL is the conductor of L
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Electronic version of an article published as "Journal of number theory", vol. 130, no 7, p. 1560-1570. DOI no 10.1016/j.jnt.2010.03.003. <http://www.uam.es/personal_pdi/ciencias/engonz/research/papers/levelBB.pdf>
CitationGonzalez, E.; Guitart, X. On the modularity level of modular abelian varieties over number fields. "Journal of number theory", Juliol 2010, vol. 130, núm. 7, p. 1560-1570. 
URIhttp://hdl.handle.net/2117/8484
DOI10.1016/j.jnt.2010.03.003
ISSN0022-314X
Publisher versionhttp://www.uam.es/personal_pdi/ciencias/engonz/research/papers/levelBB.pdf
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