  We prove vanishing results for the coherent cohomology of the good reduction
modulo $p$ of the Siegel variety with coefficients in some automorphic bundles.
We show that for an automorphic bundle with highest weight $\lambda$ near the
walls of the anti-dominant Weyl chamber, there is an integer $e \geq 0$ such
that the cohomology is concentrated in degrees $[0, e]$. The accessible weights
with our method are not necessarily regular and not necessarily $p$-small.
Since our method is technical, we also provide an algorithm written in Sage
that computes explicitly the vanishing results.
