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arXiv · 1809.00194

Structure and bases of modular space sequences $(M_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ and $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$. Part III: Cuspidal spaces

Jean-Christophe Feauveau
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Abstract

Based on the notion of strong modular form developed in Part I, we propose to structure the family of cuspidal modular form spaces $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ and to determine bases for each of these spaces, once known bases for the first values of $k$. We then apply these theoretical results to explicitly determine bases for space families $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ when $1\leq N \leq 10$.

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Jean-Christophe Feauveau. 2018-09-01. Structure and bases of modular space sequences $(M_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ and $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$. Part III: Cuspidal spaces. https://arxiv.org/abs/1809.00194

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