A_6-extensions of Q and the mod p cohomology of GL(3,Z)
  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. 
Avner Ash (Boston College), David Pollack (Wesleyan University),   Warren Sinnott (Ohio State University)