Counting absolutely cuspidals for quivers

For an arbitrary quiver \(Q=(I,\Omega )\) and dimension vector \(\mathbf {d} \in \mathbb {N}^I\) we define the dimension of absolutely cuspidal functions on the moduli stacks of representations of dimension \(\mathbf {d}\) of a quiver Q over a finite field \(\mathbb {F}_q\), and prove that it is a polynomial in q, which we conjecture to be positive and integral. We obtain a closed formula for these dimensions of spaces of cuspidals for totally negative quivers.