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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 curveassociated with $\Gamma$, and let $\overline{\mathscr{L}}^{\otimes k}$ be thelogarithmically singular metrized line bundle on $\mathscr{X}(\Gamma)$associated to modular forms of level $\Gamma$ and weight $12k$, endowed withthe 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 cuspforms of level $\Gamma$ and weight $12k$ is a euclidean lattice with respect tothe Petersson norm. In this paper, we describe the distribution of thesuccessive minima of the $\mathscr{S}_k$ as $k \to \infty$, generalizing thework of Chinburg, Guignard, and Soul\'{e} which addressed the case $\Gamma =\text{PSL}_2(\mathbb{Z})$.

Distribution of the successive minima of the Petersson norm on cusp forms