Abstract
In this article we consider the Galois representations associated by Taylor and Weissauer to a genus two Siegel cusp form f, in the case of level 1 and multiplicity one. After extending (by elementary arguments) to a set of density 1 set of primes a result ensuring maximal image obtained in a previous article, we derive two irreducibility results for these modular Galois representations. In particular we show that under some technical, effective conditions, the representations are defined over the field of coefficients of f at least for
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1Luis V. Dieulefait,Centre de Recerca Matemàtica,Apartat 50,E-08193, Bellaterra (Barcelona), Spain e-mail: Ldieulefait@crm. es
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© 2004 Springer Basel AG
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Dieulefait, L.V. (2004). Irreducibility of Galois Actions on Level 1 Siegel Cusp Forms. In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_5
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DOI: https://doi.org/10.1007/978-3-0348-7919-4_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9621-4
Online ISBN: 978-3-0348-7919-4
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