  We propose an exact, finite $N$ formula for the partition function over
$1/4^{th}$ BPS states in the conformal field theory on the world volume of $N$
coincident M5 branes and $1/8^{th}$ BPS states in the theory of $N$ coincident
M2 branes. We obtain our partition function by performing the radial
quantization of the Coulomb Branches of these theories, and rederive the same
formula from the quantization of supersymmetric giant and dual giant gravitons
in $AdS_7 \times S^4$ and $AdS_4 \times S^7$. Our partition function is
qualitatively similar to the analogous quantity in ${\cal N}=4$ Yang Mills. It
reduces to the sum over supersymmetric multi gravitons at low energies, but
deviates from this supergravity formula at energies that scale like a positive
power of $N$.
