Counting cusp forms on Sp(4)

How many cusp forms exist on SL(2), SL(n), or a more general (reductive or semi-simple) linear algebraic group? Despite the long history of research in this area, until a few years ago it was not even known that there are infinitely many cusp forms on a group such as SL(n) beyond very small values of n. A good way to answer this question is through a generalization of classical Weyl’s law from spectral theory to the automorphic setting. I will explain some of the background and results along these lines and discuss some joint work in preparation with Werner Mueller of University of Bonn, establishing Weyl's law with remainder terms for the group Sp(4).