AI 中文总结
本文针对全模群的权$k$尖点形式空间，利用素数级艾森斯坦级数构造出显式有理张成子集，核心是通过非中心二次扭$L$-值确定尖点形式，解决了相关张成集的构造问题。
AI 中文摘要
设$S_k$为全模群${\rm SL}_2(\boldsymbol{Z})$的权$k$尖点形式空间。本文将展示由素数级艾森斯坦级数构造的$S_k$的显式有理张成子集，证明的核心是通过非中心二次扭$L$-值确定尖点形式的结果。
英文摘要
Let $S_k$ be the space of cusp forms of weight $k$ for the full modular group ${\rm SL}_2(\mathbb{Z})$. 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.
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