Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Conference Paper

Mod-2 dihedral Galois representations of prime conductor


Medvedovsky,  Anna
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Supplementary Material (public)
There is no public supplementary material available

Kedlaya, K. S., & Medvedovsky, A. (2019). Mod-2 dihedral Galois representations of prime conductor. In R. Scheidler, & J. Sorenson (Eds.), Proceedings of the Thirteenth Algorithmic Number Theory Symposium (pp. 325-342). Berkeley: Mathematical Sciences Publishers.

Cite as: https://hdl.handle.net/21.11116/0000-0004-8A7C-6
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.