Structure and bases of modular space sequences (M_2k(Γ₀(N)))_{k∈ ℕ^*} and (S_2k(Γ₀(N)))_{k∈ ℕ^*}. Part II: a modular butterfly hunt

2018/09/01 by Jean-Christophe Feauveau, Feauveau, Jean-Christophe
Mathematics · #11F11 #11F33 #11G16 #33E05 #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1809.00192

openalex publication_date 2018/09/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In the first part of this article, which contains three of them, we have identified the notion of level N strong modular unit. It enabled us to structure the modular forms family (M_2k(Γ₀(N)))_{k∈ ℕ^*} and to propose the explicit bases for these spaces. It is in this perspective that we wrote this second part where the structure and explicit bases are proposed when 1≤ N ≤ 10.

Related

• Structure and bases of modular space sequences (M_2k(Γ₀(N)))_{k∈ ℕ^*} and (S_2k(Γ₀(N)))_{k∈ ℕ^*}. Part I : Strong modular units
• Structure and bases of modular space sequences (M_2k(Γ₀(N)))_{k∈ ℕ^*} and (S_2k(Γ₀(N)))_{k∈ ℕ^*}. Part III: Cuspidal spaces
• Dimension sequences of modular forms
• A new basis for the space of modular forms
• Computing bases of modular forms using the graded algebra structure