  We use the Poincar\'e series method to compute gravity partition functions
associated to SU(N) level 1 WZW models with arbitrarily large numbers of
modular invariants. The result is an average over these invariants, with the
weights being given by inverting a matrix whose size is of order the number of
invariants. For the chosen models, this matrix takes a special form that allows
us to invert it for arbitrary size and thereby explicitly calculate the weights
of this average. For the identity seed we find that the weights are positive
for all N, consistent with each model being dual to an ensemble average over
CFT's.
