Classical questions about modular forms on SL2 have direct analogues on higher-rank groups: What is the dimension of spaces of forms of a given weight and level? How are the Hecke eigenvalues distributed? What is the sign of the functional equation of the associated L-function? Though exact answers can be hard to obtain in general for groups of higher rank, I’ll describe some statistical results towards these questions, and out- line how we obtain them using the stable trace formula. This is joint work, some of it in progress, with Rahul Dalal.