  We give two proofs that appropriately defined congruence subgroups of the
mapping class group of a surface with punctures/boundary have enormous amounts
of rational cohomology in their virtual cohomological dimension. In particular
we give bounds that are super-exponential in each of three variables: number of
punctures, number of boundary components, and genus, generalizing work of
Fullarton-Putman. Along the way, we give a simplified account of a theorem of
Harer explaining how to relate the homotopy type of the curve complex of a
multiply-punctured surface to the curve complex of a once-punctured surface
through a process that can be viewed as an analogue of a Birman exact sequence
for curve complexes.
  As an application, we prove upper and lower bounds on the coherent
cohomological dimension of the moduli space of curves with marked points. For
$g \leq 5$, we compute this coherent cohomological dimension for any number of
marked points. In contrast to our bounds on cohomology, when the surface has $n
\geq1$ marked points, these bounds turn out to be independent of $n$, and
depend only on the genus.
