  Let $H<\mathrm{PSL}_2(\mathbb{Z})$ be a finite index normal subgroup which is
contained in a principal congruence subgroup, and let $\Phi(H)\neq H$ denote a
term of the lower central series or the derived series of $H$. In this paper,
we prove that the commensurator of $\Phi(H)$ in $\mathrm{PSL}_2(\mathbb{R})$ is
discrete. We thus obtain a natural family of thin subgroups of
$\mathrm{PSL}_2(\mathbb{R})$ whose commensurators are discrete, establishing
some cases of a conjecture of Shalom.
