Let $\mathcal A_{g,[n]}$ denote the moduli space of principal polarized abelian varieties with level-[n] structure and $\bar {\mathcal A}_{g,[n]}\supset \mathcal A_{g,[n]}$ a smooth Toroida compapctification. For $n$ sufficiently large, $\mathcal A_{g,[n]}$ carries a a universal family $$h: X\to \mathcal A_{g,[n]}.$$ Consider the universal locally constant sheaf $$\mathbb V=R^1h_*\mathbb Z_{\mathcal A_{g,[n]}}.$$
My question is that, whether there exists an $n$ (largely enough), such that $\mathbb V$ has unipotent local monodromy around all components of $\Delta:=\bar {\mathcal A}_{g,[n]}\setminus \mathcal A_{g,[n]}.$ Is there any reference for this question?
