Mazur’s principle for U(2,1) Shimura varieties

Mazur’s principle gives a criterion under which an irreducible mod l Galois representation arising from a classical modular form of level Np (with p prime to N) also arises from a classical modular form of level N . We consider the analogous question for Galois representations arising from certain unitary Shimura varieties. In particular, we prove an analogue of Mazur’s principle for U(2, 1) Shimura varieties. We also give a conjectural criterion for a Galois representation arising in the cohomology of a unitary Shimura variety whose level subgroup is parahoric at p to also arise in the cohomology of a Shimura variety with “less level structure at p”. 2000 MSC Classification: 11F80, 11F33, 11G18