Equivariant Cohomology of the Moduli Space of Genus Three Curves with   Symplectic Level Two Structure via Point Counts
  We make cohomological computations related to the moduli space of genus three curves with symplectic level two structure by means of counting points over finite fields. In particular, we determine the cohomology groups of the quartic locus as representations of the symmetric group on seven elements. 
Olof Bergvall
math.AG math.NT