  Thanks to the Harder-Eichler-Shimura isomorphism we can realize a
quaternionic automorphic representation of a fixed weight in the cohomology
space of certain arithmetic groups. For many interesting applications, it is
convenient to consider the cap-product of a cohomology class in these spaces
with a fundamental class associated to a maximal torus. In a recent paper, the
author computes the absolute value of such a cap-product, and he relates it to
special values of Rankin-Selberg L-functions. This provides a formula analogous
to that of Waldspurger in higher cohomology. In this paper we compute the
square of the cap-product instead of its absolute value.
