I've been reading a preprint by David Hansen (with appendix by James Newton) called Universal eigenvarieties, trianguline Galois representations and p-adic Langlands functoriality. In it he talks about using overconvergent cohomology to construct eigenvarieties.
Now I was wondering if I could get a reference/ explanation as to why these eigenvarieties will be related to the ones one make coming from overconvergent modular forms (as in Kevin Buzzard's- Eigenvarieties) I don't quite see the relation between this OC cohomology and OC modular forms. I have a feeling it has something to do (as I think Hansen says on p42) with the classical Eichler--Shimura and Theorem 3.2.5 on the above paper, which is a generalization of Stevens control theorem. But it's not clear to me what the relation is.