  We consider two types of quotients of the integrable modules of $\hat{sl}_2$.
These spaces of coinvariants have dimensions described in terms of the Verlinde
algebra of level-$k$. We describe monomial bases for the spaces of
coinvariants, which leads to a fermionic description of these spaces. For
$k=1$, we give the explicit formulas for the characters. We also present
recursion relations satisfied by the characters and the monomial bases.
