  We extend to positive real weights Haberland's formula giving a cohomological
description of the Petersson scalar product of modular cusp forms of positive
even weight. This relation is based on the cup product of an Eichler cocycle
and a Knopp cocycle. We also consider the cup product of two Eichler cocycles
attached to modular forms. In the classical context of integral weights at
least $2$ this cup product is uninteresting. We show evidence that for real
weights this cup product may very well be non-trivial. We approach the question
whether the cup product is a non-trivial coinvariant by duality with a space of
entire modular forms. Under suitable conditions on the weights this leads to an
explicit triple integral involving three modular forms. We use this
representation to study the cup product numerically.
