Geodesic
Dihedral Galois representations and Katz modular forms
Documenta mathematica, Tome 9 (2004), pp. 123-133
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We show that any two-dimensional odd dihedral representation ρ over 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 ε and weight k, where N is the conductor, ε is 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 ρ is unramified at p. Direct arguments are used in the exceptional cases, where general results on weight and level lowering are not available.
DOI : 10.4171/dm/160
Classification : 11F11, 11F80, 14G35 
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     author = {Gabor Wiese},
     title = {Dihedral {Galois} representations and {Katz} modular forms},
     journal = {Documenta mathematica},
     pages = {123--133},
     year = {2004},
     volume = {9},
     doi = {10.4171/dm/160},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/160/}
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Gabor Wiese. Dihedral Galois representations and Katz modular forms. Documenta mathematica, Tome 9 (2004), pp. 123-133. doi: 10.4171/dm/160

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