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.