  We determine, in two independent ways, the number of BPS quantum states
arising from supergravity degrees of freedom in a system with fixed total D4D0
charge. First, we count states generated by quantizing the spacetime degrees of
freedom of 'entropyless' multicentered solutions consisting of anti-D0-branes
bound to a D6-anti-D6 pair. Second, we determine the number of free
supergravity excitations of the corresponding AdS_3 geometry with the same
total charge. We find that, although these two approaches yield a priori
different sets of states, the leading degeneracies in a large charge expansion
are equal to each other and that, furthermore, the number of such states is
parametrically smaller than that arising from the D4D0 black hole's entropy.
This strongly suggests that supergravity alone is not sufficient to capture all
degrees of freedom of large supersymmetric black holes. Comparing the free
supergravity calculation to that of the D6-anti-D6-D0 system we find that the
bound on the free spectrum imposed by the stringy exclusion principle (a
unitarity bound in the dual CFT) seems to be captured in the dynamics of the
fully interacting but classcial supergravity equations of motion.
