Sur la cohomologie des syst\`emes locaux sur les espaces des modules des courbes de genre 2 et des surfaces ab\'eliennes

We consider the cohomology of local systems on the moduli space of curves of genus 2 and the moduli space of abelian surfaces. We give an explicit formula for the Eisenstein cohomology and a conjectural formula for the endoscopic contribution. We show how counting curves over finite fields provides us with detailed information about Siegel modular forms.