  This work gives a version of the Eichler-Shimura isomorphism with a
non-abelian $H^1$ in group cohomology. Manin has given a map from vectors of
cusp forms to a noncommutative cohomology set by means of iterated integrals.
We show Manin's map is injective but far from surjective. By extending Manin's
map we are able to construct a bijective map and remarkably this establishes
the existence of a non-abelian version of the Eichler-Shimura map.
