  We study the Virasoro conformal block decomposition of the genus two
partition function of a two-dimensional CFT by expanding around a Z3-invariant
Riemann surface that is a three-fold cover of the Riemann sphere branched at
four points, and explore constraints from genus two modular invariance and
unitarity. In particular, we find 'critical surfaces' that constrain the
structure constants of a CFT beyond what is accessible via the crossing
equation on the sphere.
