Explicit calculations of automorphic forms for definite unitary groups
Abstract
I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U_1 x U_1 x U_1 and U_1 x U_2, and to an example of a non-endoscopic form of weight (3,3) corresponding to a family of 3-dimensional irreducible l-adic Galois representations. I also compute the 2-adic slopes of some automorphic forms with level structure at 2, giving evidence for the local constancy of the slopes.
Cite
@article{arxiv.0801.3176,
title = {Explicit calculations of automorphic forms for definite unitary groups},
author = {David Loeffler},
journal= {arXiv preprint arXiv:0801.3176},
year = {2011}
}
Comments
This version fixes an error pointed out by my PhD examiners -- the previous version cited a form of Ramanujan's conjecture which is in fact false. Accompanying computer programs available from http://www.ma.ic.ac.uk/~dl505/