  A formula for the exact partition function of 1/4 BPS dyons in a class of CHL
models has been proposed earlier. The formula involves inverse of Siegel
modular forms of subgroups of Sp(2,Z). In this paper we propose product
formulae for these modular forms. This generalizes the result of Borcherds and
Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2,Z) group.
