In this paper we introduce a certain space of higher order modular forms of
weight 0 and show that it has a Hodge structure coming from the geometry of the
fundamental group of a modular curve. This generalizes the usual structure on
classical weight 2 forms coming from the cohomology of the modular curve.
Further we construct some higher order Poincare series to get higher order
higher weight forms and using them we define a space of higher weight, higher
order forms which has a mixed Hodge structure as well.