Abstract:

We will discuss an approach to compute dimensions of certain spaces of classical Siegel modular forms. This leads to the question of dimensions of fixed vectors under certain sequences of congruence subgroups in representations of p-adic GSp(4). For general representations, these dimensions remain unknown. We will illustrate the situation in the special case of depth-zero supercuspidal representations; these include the first examples of (generic) representations for which the fixed-vector dimensions have been computed.