  In this paper, we construct a pairing between modular forms of positive real
weight and elements of certain Eichler cohomology groups that were introduced
by Knopp in 1974. We use spectral theory of automorphic forms to show that this
pairing is perfect for all positive weights except 1. The approach in this
paper gives a new proof of a theorem by Knopp and Mawi from 2010 for all real
weights excluding 1 and also a version of this theorem for vector-valued
modular forms.
