Dimension sequences of modular forms

2025/07/16 by Erick Ross, Ross, Erick · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.12340

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

For N ≥ 1, let S₂^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 S₂^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.

Citations

• Non-repetition of second coefficients of Hecke polynomials
• Asymptotics and sign patterns of Hecke polynomial coefficients
• Nonvanishing of Second Coefficients of Hecke Polynomials on the Newspace
• Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces
• Distinguishing newforms
• On the genera of X₀(N)

Cited by

• Dimensions of spaces of modular forms

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