Holomorphic modular forms and cocycles

I'll speak about joint work with YoungJu Choie and Nikos Diamantis on
the cocycles that one can attach to holomorphic modular forms. Knopp
has shown that there is a generalization of the classical
Eichler-Shimura theory tocusp forms of real weight. We consider a map
to cohomology from the space of holomorphic functions with modular
transformation behavior (without any growth condition at the cusps).
For weights that are not integers at least two the results differ
considerably from the classical Eichler-Shimura theory, and are
analogous to earlier results for Maass wave forms studied by Don
Zagier, John Lewis and me.