Codimensions one and two cohomology of Hecke congruence subgroups

For $n\ge 1$ and $p$ a prime, the Hecke congruence subgroup ${\mathrm{\Gamma }}_{0,n}(p)\le {\mathrm{S}\mathrm{L}}_n(\mathbb{Z})$ is the subgroup of matrices whose first column is of the form $(\ast ,0,\dots ,0{)}^{t}p$. Borel–Serre showed that ${\mathrm{\Gamma }}_{0,n}(p)$ has virtual cohomological dimension $\left(\genfrac{}{}{0px}{}{n}{2}\right)$. The first author proved that the rational cohomology in this top degree $\left(\genfrac{}{}{0px}{}{n}{2}\right)$ vanishes for $n$ sufficiently large compared to $p$. We prove analogous results in codimension $1$ and $2$.