Siegel paramodular forms and sparseness in AdS₃/CFT₂

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 AdS₃ ×S³ ×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 AdS₃/CFT₂.