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Dihedral Galois representations and Katz modular forms

Gabor Wiese
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Abstract

We show that any two-dimensional odd dihedral representation ρover a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character εand weight k, where N is the conductor, εis the prime-to-p part of the determinant and k is the so-called minimal weight of ρ. In particular, k=1 if and only if ρis unramified at p. Direct arguments are used in the exceptional cases, where general results on weight and level lowering are not available.

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Gabor Wiese. 2004-02-10. Dihedral Galois representations and Katz modular forms. https://arxiv.org/abs/math/0402163

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