CFT OPE coefficients from modularity

We shall review the derivation of Cardy like formula for averaged three point coefficients in two dimensional conformal field theories, starting from the torus one point function and look at its holographic interpretation. Next we shall exploit the modular property of the four point correlator on the plane (as a consequence of the crossing symmetry) to further constrain the averaged three point coefficients and make contact with the black hole S-matrix.