### Galois representations with conjectural connections to arithmetic cohomology, by Avner Ash, Darrin Doud, and David Pollack

In this paper we extend a conjecture of Ash and Sinnott relating
niveau one Galois representation to the mod p cohomology of
congruence subgroups of SL(n,Z) to include Galois representations
of higher niveau. We then present computational evidence for our
conjecture in the case n=3 in the form of three-dimensional Galois
representations which appear to correspond to cohomology eigenclasses
as predicted by the conjecture. Our examples include Galois
representations with nontrivial weight and level, as well as
irreducible three-dimensional representations which are in no obvious
way related to lower dimensional representations. In addition, we
prove that certain symmetric square representations are actually
attached to cohomology eigenclasses predicted by the conjecture.

Avner Ash, Darrin Doud, and David Pollack <doud@math.harvard.edu>