Terminology question for the cohomology of the Hilbert modular group

Question

Let $\Gamma$ be the Hilbert modular group of determinant one matrices with entries in the ring of integers of a real quadratic field $F$, and let $M$ be a $\Gamma$-module. Is there a standard name for the subgroup of $H^i(\Gamma,M)$ consisting of classes that vanish at all the stabilisers of elements of $P^1(F)$? When $F=\mathbb Q$, one calls this the parabolic cohomology but the terminology is less justified in this case since the stabilisers now consist of more than just parabolic elements.