Possible connection between a generalized Maeda's conjecture and local types
Number Theory
2016-08-19 v1
Abstract
Here we follow on the proposed generalization of Maeda's conjecture made in [2]. We report on computations that suggest a relation between the number of local types and the number of non-CM newform Galois orbits. We extend the conjecture into spaces with non-trivial Nebentypus and provide a formula for the number of non-CM orbits for all levels and trivial Nebentypus. We also provide some numerical evidence towards further generalizations of this conjecture to totally real fields as well as further strengthening of it by proposing a structure for the corresponding Galois groups.
Cite
@article{arxiv.1608.05285,
title = {Possible connection between a generalized Maeda's conjecture and local types},
author = {Luis Dieulefait and Panagiotis Tsaknias},
journal= {arXiv preprint arXiv:1608.05285},
year = {2016}
}
Comments
A version 2 will soon appear with the computations of the number of local types being included