Affine Stratification of $\mathcal A_4$

We construct an affine stratification for $\mathcal A_4(\mathbb C)$ of length 6, in the sense of Roth and Vakil, which gives us an upper bound of 6 for the cohomological dimension of $\mathcal A_4(\mathbb C)$. We conjecture that in general for arbitrary $g$ the cohomological dimension of $\mathcal A_g$ is equal to $g(g-1)/2$.