The title says the question. For a quiver and a dimension vector and a stability vector, we can construct a moduli space of semistable quiver representations with the given dimension vector. The question is about the dimension of this moduli space. We can consider over $\mathbb{C}$.
A quick search discovers nothing relevant. I reckon this an open problem for a general quiver and dimension vector. So I also want to know anything results for special quivers.