On modular representations of $$(\bar Q/Q)$$ arising from modular forms

@article{Ribet1990OnMR,
  title={On modular representations of
\$\$(\bar Q/Q)\$\$
 arising from modular forms},
  author={Kenneth A. Ribet},
  journal={Inventiones mathematicae},
  year={1990},
  volume={100},
  pages={431-476}
}
  • K. Ribet
  • Published 1 December 1990
  • Mathematics
  • Inventiones mathematicae
where G is the Galois group GaI ( I ) /Q) and F is a finite field of characteristic I > 3. Suppose that p is modular of level N, i.e., that it arises from a weight-2 newform of level dividing N and trivial "Nebentypus character." Then p is an odd representation: the matrix p(c) (where c is a complex conjugation in G) has eigenvalues + 1, 1. Since + 1 and 1 are distinct in F, p is absolutely irreducible and has a model over every subfield of F containing the set trace(p ). We assume that F has… Expand
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