  We study the topology dependence of finite size corrections to the Ising
model partition function by considering the model on a triangular lattice
embedded on a genus two surface. At criticality we observe a universal shape
dependent correction, expressible in terms of Riemann theta functions, that
reproduces the modular invariant partition function of the corresponding
conformal field theory. The period matrix characterizing the moduli parameters
of the limiting Riemann surface is obtained by a numerical study of the lattice
continuum limit. The same results are reproduced using a discrete holomorphic
structure.
