Automorphic Forms on Feit's Hermitian Lattices
Number Theory
2019-04-17 v3
Abstract
We consider the genus of classes of unimodular Hermitian lattices of rank over the Eisenstein integers. This set is the domain for a certain space of algebraic modular forms. We find a basis of Hecke eigenforms, and guess global Arthur parameters for the associated automorphic representations, which recover the computed Hecke eigenvalues. Congruences between Hecke eigenspaces, combined with the assumed parameters, recover known congruences for classical modular forms, and support new instances of conjectured Eisenstein congruences for automorphic forms.
Cite
@article{arxiv.1804.05884,
title = {Automorphic Forms on Feit's Hermitian Lattices},
author = {Neil Dummigan and Sebastian Schönnenbeck},
journal= {arXiv preprint arXiv:1804.05884},
year = {2019}
}