For n at most 3, we determine the relevant terms of the point count of $$M_{4,n}$$ over finite fields ($$S_n$$-equivariantly). Using several earlier results, we then determine the cohomology of $$\overline{M}_{4,n}$$ and the full count for $$M_{4,n}$$ and we deduce the mentioned vanishing for all g and n.