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arXiv · 1806.04653

Mod-2 dihedral Galois representations of prime conductor

Kiran S. Kedlaya·Anna Medvedovsky
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Abstract

For all odd primes N up to 500000, we compute the action of the Hecke operator T_2 on the space S_2(Gamma_0(N), Q) and determine whether or not the reduction mod 2 (with respect to a suitable basis) has 0 and/or 1 as eigenvalues. We then partially explain the results in terms of class field theory and modular mod-2 Galois representations. As a byproduct, we obtain some nonexistence results on elliptic curves and modular forms with certain mod-2 reductions, extending prior results of Setzer, Hadano, and Kida.

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Kiran S. Kedlaya, Anna Medvedovsky. 2018-06-12. Mod-2 dihedral Galois representations of prime conductor. https://doi.org/10.2140/obs.2019.2.325

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