  Genus two partition functions of 2d chiral conformal field theories are given
by Siegel modular forms. We compute their conformal blocks and use them to
perform the conformal bootstrap. The advantage of this approach is that it
imposes crossing symmetry of an infinite family of four point functions and
also modular invariance at the same time. Since for a fixed central charge the
ring of Siegel modular forms is finite dimensional, we can perform this
analytically. In this way we derive bounds on three point functions and on the
spectrum of such theories.
