Explicit calculations of automorphic forms for definite unitary groups
David Loeffler
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
G(hat{Z}) 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 U1 x U1
x U1 and U1 x U1, 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.
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