Abstract：

Some Shimura varieties can be interpreted as moduli spaces of curves. In such cases this can be used to get information about modular forms. We discuss a ball quotient related to moduli of curves of genus three. We study cohomology of local systems and calculate the traces of Hecke operators by counting points on curves over finite fields. We also construct all vector-valued Picard modular forms using invariant theory. This is joint work with Jonas Bergstroem and Fabien Clery.