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A non-solvable extension of ℚ unramified outside 7

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  24 January 2012

Luis V. Dieulefait
Luis V. Dieulefait*
Affiliation:
Departament d’Álgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain (email: ldieulefait@ub.edu)
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Abstract

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We consider a mod 7 Galois representation attached to a genus 2 Siegel cusp form of level 1 and weight 28 and using some of its Fourier coefficients and eigenvalues computed by N. Skoruppa and the classification of maximal subgroups of PGSp(4,p) we show that its image is as large as possible. This gives a realization of PGSp(4,7) as a Galois group over ℚ and the corresponding number field provides a non-solvable extension of ℚ which ramifies only at 7.

Keywords

Galois theoryGalois representationsSiegel modular forms

MSC classification

Secondary: 11F80: Galois representations 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 669 - 674
Copyright
Copyright © Foundation Compositio Mathematica 2012

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