182 research outputs found
A non-solvable extension of \Q unramified outside 7
We consider a mod 7 Galois representation attached to a genus 2 Siegel
cuspforms 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
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