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September 10, 2025Open Access

Dimension sequences of modular forms

Key Points

The conjectured dimension of the newspace of modular forms takes on all natural numbers.
The complete characterization is achieved for the variations of this modular forms problem.
The study focuses on cuspidal modular forms of weight 2 and level N to determine significant properties.
The findings may uncover deeper insights into modular forms and their dimensions relevant to number theory.

Abstract

Abstract For N 1 N ≥ 1, let S₂^ { new } (N) S 2 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, S₂^ { new } (N) dim S 2 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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Cite This Study

Erick Ross (Wed,) studied this question.

synapsesocial.com/papers/68c1b81f54b1d3bfb60ec679 https://doi.org/https://doi.org/10.1007/s40993-025-00659-1