  Let $\Gamma \subseteq \text{PSL}_2(\mathbb{Z})$ be a finite index subgroup.
Let $\mathscr{X}(\Gamma)$ be a regular proper model of the modular curve
associated with $\Gamma$, and let $\overline{\mathscr{L}}^{\otimes k}$ be the
logarithmically singular metrized line bundle on $\mathscr{X}(\Gamma)$
associated to modular forms of level $\Gamma$ and weight $12k$, endowed with
the Petersson metric. For each $k \geq 1$, the sub-lattice $\mathscr{S}_k
\subseteq H^0(\mathscr{X}(\Gamma), \mathscr{L}^{\otimes k})$ of integral cusp
forms of level $\Gamma$ and weight $12k$ is a euclidean lattice with respect to
the Petersson norm. In this paper, we describe the distribution of the
successive minima of the $\mathscr{S}_k$ as $k \to \infty$, generalizing the
work of Chinburg, Guignard, and Soul\'{e} which addressed the case $\Gamma =
\text{PSL}_2(\mathbb{Z})$.
