  We study symmetric products of the chiral 'Monster' conformal field theory
with c=24 in the grand canonical ensemble by introducing a complex parameter
\rho, whose imaginary part represents the chemical potential \mu conjugate to
the number of copies of the CFT. The grand canonical partition function is
given by the DMVV product formula in terms of the multiplicities of the seed
CFT. It possesses an O(2,2;\ZZ) symmetry that enhances the familiar SL(2,\ZZ)
modular invariance of the canonical ensemble and mixes the modular parameter
\tau with the parameter \rho. By exploiting this enhanced modular symmetry and
the pole structure of the DMVV product formula we are able to extend the region
of validity of Cardy's formula, and explain why it matches the semi-classical
Bekenstein-Hawking formula for black holes all the way down to the AdS-scale.
We prove that for large c the spectrum contains a universal perturbative sector
whose degeneracies obey Hagedorn growth. The transition from Cardy to Hagedorn
growth is found to be due to the formation of a Bose-Einstein condensate of
ground state CFTs at low temperatures. The grand canonical partition function
has an interesting phase structure, which in addition to the standard
Hawking-Page transition between low and high temperature, exhibits a
wall-crossing transition that exchanges the roles of \tau and \rho.
