  We discuss the application of Siegel paramodular forms to the counting of
polar states in symmetric product orbifold CFTs. We present five special
examples and provide exact analytic counting formulas for their polar states.
The first example reproduces the known result for type IIB supergravity on
AdS$_3\times S^3\times K3$, whereas the other four examples give new counting
formulas. Their crucial feature is that the low energy spectrum is very sparse,
which suggests the existence of a suitable dual supergravity theory. These
examples open a path to novel realizations of AdS$_3$/CFT$_2$.
