  We present six examples of 3-dimensional mod p Galois representations of type
A_6 for which we were able to obtain computational evidence for the
generalization of Serre's Conjecture proposed by Ash, Doud, Pollack, and
Sinnott. We also propose a further refinement of the conjecture corresponding
to the "peu vs. tr`es ramifi'ee" distinction of Serre.
