Provides traces of Hecke operators on spaces of scalar- and vector-valued Siegel modular forms of degree 2 (levels 1 and 2) and degree 3 (level 1), derived from counts of curves over finite fields and their cohomological interpretation by Bergström, Faber and van der Geer, together with dimension tables, data on forms related to G2, congruences, and Fourier expansions of degree 2 forms of level 1. For degree 2 the traces are unconditional; the degree 3 data rests on conjectures of Bergström-Faber-van der Geer.