Structure and bases of modular spaces sequences $(M_{2k}(\Gamma _0(N)))_{k\in \protect \mathbb{N}^*}$

Jean-Christophe Feauveau

doi:10.5802/ambp.395

Structure and bases of modular spaces sequences

{(M_{2 k} (Γ_{0} (N)))}_{k \in ℕ^{*}}

[Structure et bases des suites d’espaces modulaires

{(M_{2 k} (Γ_{0} (N)))}_{k \in ℕ^{*}}

]

Jean-Christophe Feauveau ¹

¹ Lycée Bellevue, 135, route de Narbonne BP. 44370 31031 Toulouse Cedex 4 France

Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 2, pp. 181-206.

Résumé
Abstract

Le discriminant modulaire $Δ$ est connu pour structurer la famille de formes modulaires de niveau 1, ${(M_{2 k} ({SL}_{2} (ℤ)))}_{k \in ℕ^{*}}$ . Pour tout entier $N$ , nous définissons une unité modulaire forte de niveau $N$ notée $Δ_{N}$ , qui permet de structurer la famille ${(M_{2 k} (Γ_{0} (N)))}_{k \in ℕ^{*}}$ de manière identique. Nous appliquerons ce résultat à la recherche de bases pour chacun des espaces ${(M_{2 k} (Γ_{0} (N)))}_{k \in ℕ^{*}}$ .

The modular discriminant $Δ$ is known to structure the sequence of modular forms of level $1$ ${(M_{2 k} ({SL}_{2} (ℤ)))}_{k \in ℕ^{*}}$ . For any positive integer $N$ , we define a strong modular unit $Δ_{N}$ of level $N$ which enables us to structure the sequence ${(M_{2 k} (Γ_{0} (N)))}_{k \in ℕ^{*}}$ in an identical way. We then apply this novel result to the search of bases for each of the ${(M_{2 k} (Γ_{0} (N)))}_{k \in ℕ^{*}}$ spaces.

Publié le : 2021-03-09

DOI : 10.5802/ambp.395

Classification : 11F11, 11G16, 11F33, 33E05
Keywords: modular forms, modular units, Dedekind eta function
Mot clés : formes modulaires, unités modulaires, fonction de Dedekind

Affiliations des auteurs :

Jean-Christophe Feauveau ¹

¹ Lycée Bellevue, 135, route de Narbonne BP. 44370 31031 Toulouse Cedex 4 France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Jean-Christophe Feauveau},
     title = {Structure and bases of modular spaces sequences $(M_{2k}(\Gamma _0(N)))_{k\in \protect \mathbb{N}^*}$},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {181--206},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {27},
     number = {2},
     year = {2020},
     doi = {10.5802/ambp.395},
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     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.395/}
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Jean-Christophe Feauveau. Structure and bases of modular spaces sequences $(M_{2k}(\Gamma _0(N)))_{k\in \protect \mathbb{N}^*}$. Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 2, pp. 181-206. doi : 10.5802/ambp.395. https://ambp.centre-mersenne.org/articles/10.5802/ambp.395/

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