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arXiv · 2507.12340

Dimension sequences of modular forms

Erick Ross
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Abstract

For $N \geq 1$, let $S_{2}^{\text{new}}(N)$ denote the newspace of cuspidal modular forms of weight $2$ and level $N$. In 2004, Greg Martin conjectured that as a sequence in $N$, $\dim S_2^{\text{new}}(N)$ takes on all possible natural numbers. In this paper, we investigate several generalizations and variations of this type of problem. In each case, we provide a complete characterization of when such a property holds.

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Erick Ross. 2025-07-16. Dimension sequences of modular forms. https://arxiv.org/abs/2507.12340

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