Let K be the totally real cubic field of discriminant 49, let O be its ring
of integers, and let p be the prime over 7. Let Gamma (p)\subset Gamma =
SL_2(O) be the principal congruence subgroup of level p. This paper
investigates the geometry of the Hilbert modular threefold attached to Gamma
(p) and some related varieties. In particular, we discover an octic in P^3 with
84 isolated singular points of type A_2.

We report on the computation of torsion in certain homology theories of
congruence subgroups of SL(4,Z). Among these are the usual group cohomology,
the Tate-Farrell cohomology, and the homology of the sharbly complex. All of
these theories yield Hecke modules. We conjecture that the Hecke eigenclasses
in these theories have attached Galois representations. The interpretation of
our computations at the torsion primes 2,3,5 is explained. We provide evidence
for our conjecture in the 15 cases of odd torsion that we found in levels up to
31.