Modular forms for genus 2 and 3

The best-known modular forms are elliptic modular forms;
a natural generalization are vector-valued Siegel modular forms of genus g.
For genus 2 and 3 these modular forms are intimately connected with
the moduli of curves of genus 2 and 3. We give an explicit way to
describe such vector-valued modular forms for genus 2 and 3
using invariant theory and give some applications.
This is based on joint work with Fabien Clery and Carel Faber.