Dimensions of spaces of modular forms

Andrew R. Booker; Min Lee

Dimensions of spaces of modular forms

Number Theory 2025-12-16 v1

Authors: Andrew R. Booker , Min Lee

Abstract

We prove a conjecture of Ross concerning the value distribution of $\dim S_2^{\rm new}(\Gamma_0(N))$ for $N\in\mathbb{N}$ , as well as analogous results for general weight $k\in2\mathbb{N}$ and the full and twist-minimal spaces $S_k(\Gamma_0(N))$ , $S_k^{\rm min}(\Gamma_0(N))$ .

Keywords

modular forms dimensions of spaces newforms Gamma_0(N) weight k value distribution twist-minimal spaces

Cite

@article{arxiv.2512.12546,
  title  = {Dimensions of spaces of modular forms},
  author = {Andrew R. Booker and Min Lee},
  journal= {arXiv preprint arXiv:2512.12546},
  year   = {2025}
}

Comments

9 pages

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