  We construct the genus two (or two loop) partition function for meromorphic
bosonic conformal field theories. We use a sewing procedure involving two genus
one tori by exploiting an explicit relationship between the genus two period
matrix and pinching modular parameters. We obtain expressions for the partition
function for the chiral bosonic string, even rank lattice theories and
self-dual meromorphic conformal field theories including the Moonshine Module.
In particular, we find that for self-dual theories with central charge 24, the
genus two partition function multiplied by a universal holomorphic function of
the moduli is given by a meromorphic Siegel modular form of weight 2 where this
universal function includes ghost contributions. We also discuss a novel
expansion for certain Siegel modular forms.
