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New forms and Galois representations of octahedral type. (Formes primitives et représentations galoisiennes de type octaédral.) (French) Zbl 1053.11524

Summary: It is known by a result of Langlands and Weil that one can associate to each representation of the absolute Galois group of \(Q\) with odd determinant and octahedral type a newform of weight one. Using the work of Bayer and Frey, we provide a method for constructing such newforms. The calculation of the coefficients of their Fourier expansions at infinity can then be computed so as to provide tables. The case of forms of even level is studied in detail.

MSC:

11F80 Galois representations
11R32 Galois theory
11R39 Langlands-Weil conjectures, nonabelian class field theory

Software:

PARI/GP
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References:

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