Recovering modular forms and representations from tensor and symmetric powers

Details Recovering modular forms and representations from tensor and symmetric powers Recovering modular forms and representations from tensor and symmetric powers

2004-10-18

arxiv.org/abs/math/0410387v1

Mathematics

Number Theory

18 pages; this is a revised version of a paper submitted to the old Number Theory archive as ANT-0357

Scientific paper

We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide. Combined with refinements of strong multiplicity one, we show that if the characters of some tensor or symmetric powers of two absolutely irreducible $l$-adic representation with the algebraic envelope of the image being connected, agree at the Frobenius elements corresponding to a set of places of positive upper density, then the representations are twists of each other by a finite order character.

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