  We compute some Hodge and Betti numbers of the moduli space of stable rank
$r$ degree $d$ vector bundles on a smooth projective curve. We do not assume
$r$ and $d$ are coprime. In the process we equip the cohomology of an arbitrary
algebraic stack with a functorial mixed Hodge structure. This Hodge structure
is computed in the case of the moduli stack of rank $r$, degree $d$ vector
bundles on a curve. Our methods also yield a formula for the Poincare
polynomial of the moduli stack that is valid over any ground field.
