  We prove that there exist exactly eight Siegel modular forms with respect to
the congruence subgroups of Hecke type of the paramodular groups of genus two
vanishing precisely along the diagonal of the Siegel upper half-plane. This is
a solution of a question formulated during the conference "Black holes, Black
Rings and Modular Forms" (ENS, Paris, August 2007). These modular forms
generalize the classical Igusa form and the forms constructed by Gritsenko and
Nikulin in 1998.
