  The moduli space of twisted stable maps into the stack $B(\Z/m\Z)^2$ carries
a natural $S_n$-action and so its cohomology may be decomposed into irreducible
$S_n$-representations. Working over $\Spec \Z[1/m]$ we show that the
alternating part of the cohomology of one of its connected components is
exactly the cohomology associated to cusp forms for $\Gamma(m)$. In particular
this offers an alternative to Scholl's construction of the Chow motive
associated to such cusp forms. This answers in the affirmative a question of
Manin on whether one can replace the Kuga-Sato varieties used by Scholl with
some moduli space of pointed stable curves.
