A theorem of Eichler and Shimura says that the space of cusp forms with complex coefficients appears as a direct summand of the cohomology of the compactified modular curve. Ohta has proven an analog of this theorem for the space of ordinary p-adic cusp forms with integral coefficients. Ohta's result has important applications in the Iwasawa theory of cyclotomic fields.

We discuss a new proof of Ohta's result using the geometry of Hecke correspondences at places of bad reduction.