  We prove that there are only finitely many isometry classes of even lattices
$L$ of signature $(2,n)$ for which the space of cusp forms of weight $1+n/2$
for the Weil representation of the discriminant group of $L$ is trivial. We
compute the list of these lattices. They have the property that every Heegner
divisor for the orthogonal group of $L$ can be realized as the divisor of a
Borcherds product. We obtain similar classification results in greater
generality for finite quadratic modules.
