  We prove the following theorem: Let $\bar\F_p$ be an algebraic closure of a
finite field of characteristic $p$. Let $\rho$ be a continuous homomorphism
from the absolute Galois group of $\Q$ to $\GL(3,\bar\F_p)$ which is isomorphic
to a direct sum of a character and a two-dimensional odd irreducible
representation. Under the condition that the conductor of $\rho$ is squarefree,
we prove that $\rho$ is attached to a Hecke eigenclass in the homology of an
arithmetic subgroup $\Gamma$ of $\GL(3,\Z)$. In addition, we prove that the
coefficient module needed is, in fact, predicted by a conjecture of Ash, Doud,
Pollack, and Sinnott.
