On modular mod $\ell$ Galois representations with exceptional images

Details On modular mod $\ell$ Galois representations with exceptional images On modular mod $\ell$ Galois representations with exceptional images

2003-11-06

arxiv.org/abs/math/0311082v1

Mathematics

Number Theory

This is a revised version of a preprint that first occurred elsewhere in June, 2000

Scientific paper

We give a parametrization of the possible Serre invariants $(N,k,\nu)$ of modular mod $\ell$ Galois representations of the exceptional types $A_4$, $S_4$, $A_5$, in terms of local data attached to the fields cut out by the associated projective representations. We show how this result combined with certain global considerations leads to an effective procedure that will determine for a given eigenform $f$ and prime $\ell$ whether a mod $\ell$ representation attached to $f$ is exceptional. We illustrate with numerical examples.

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