Mod-2 dihedral Galois representations of prime conductor
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866913585543774208 |
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| author | Kedlaya, Kiran S. Medvedovsky, Anna |
| author_facet | Kedlaya, Kiran S. Medvedovsky, Anna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_04653 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Mod-2 dihedral Galois representations of prime conductor Kedlaya, Kiran S. Medvedovsky, Anna Number Theory Algebraic Geometry 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. |
| title | Mod-2 dihedral Galois representations of prime conductor |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/1806.04653 |