Cohomology of arithmetic subgroups, with coefficients being algebraic representations of the corresponding reductive group, has played an importatnt role in the construction of Langlands correspondence. Traditionally the first step to access these objects is to view them as cohomology of (locally constant) sheaves on locally symmetric spaces and hence connect them with spaces of functions. However, sometimes infinite dimensional coeffients also naturallhy arise, e.g. when you try to attach elliptic curves to weight 2 eigenforms on GL_2/an imaginary cubic field, and the sheaf theoretic viewpoint might no longer be fruitful. In this talk we'll explain a different but very simple understanding of the connection between arithmetic group cohomology (with finite dimensional coefficients) and function spaces, and discuss the application of this idea to infinite dimensional coeffients.