Rational spanning sets of level-one cusp forms from Eisenstein series at prime levels

2026/08/04 by Tianyu Ni
Mathematics · #math.NT

paper · pdf

12 pages, submitted

arxiv created 2026/08/04 · arxiv updated 2026/08/06

Abstract

Let S_k be the space of cusp forms of weight k for the full modular group \rm SL₂(ℤ). In this paper, we will exhibit an explicit rational spanning subset of S_k constructed from Eisenstein series at prime levels. The main ingredient of our proof is to show a result on determining cusp forms by noncentral quadratic-twist L-values.

Citations

• Twisted periods of modular forms
• Subspaces spanned by eigenforms with nonvanishing twisted central L-values
• Distinguishing Hermitian cusp forms of degree 2 by a certain subset of all Fourier coefficients
• Twisted Hecke L-values and period polynomials
• Determination of modular forms by twists of critical L-values
• Heegner points and derivatives ofL-series