Dimensions of spaces of modular forms

2025/12/14 by Andrew R. Booker, Min Lee, Booker, Andrew R. +1
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2512.12546

Abstract

We prove a conjecture of Ross concerning the value distribution of dim S₂^{\rm new}(Γ₀(N)) for N∈ℕ, as well as analogous results for general weight k∈2ℕ and the full and twist-minimal spaces S_k(Γ₀(N)), S_k^{\rm min}(Γ₀(N)).

Citations

• Dimension sequences of modular forms
• Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces
• Missing class groups and class number statistics for imaginary quadratic fields
• A remark on the Wiener-Ikehara Tauberian theorem

Related

• Dimension sequences of modular forms
• Dimensions of the Spaces of Cusp Forms and Newforms on Gamma₀(N) and Gamma₁(N)
• Dimension Formulae for Spaces of Lifted Bianchi Modular Forms
• Large values of modular forms
• Multiplicities of representations in spaces of modular forms