Structure and bases of modular spaces sequences (M 2k (Γ 0 (N))) k *
Annales mathématiques Blaise Pascal, Volume 27 (2020) no. 2, pp. 181-206.

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

Le discriminant modulaire Δ est connu pour structurer la famille de formes modulaires de niveau 1, (M 2k (SL 2 ())) k * . Pour tout entier N, nous définissons une unité modulaire forte de niveau N notée Δ N , qui permet de structurer la famille (M 2k (Γ 0 (N))) k * de manière identique. Nous appliquerons ce résultat à la recherche de bases pour chacun des espaces (M 2k (Γ 0 (N))) k * .

Published online:
DOI: 10.5802/ambp.395
Classification: 11F11,  11G16,  11F33,  33E05
Keywords: modular forms, modular units, Dedekind eta function
Jean-Christophe Feauveau 1

1 Lycée Bellevue, 135, route de Narbonne BP. 44370 31031 Toulouse Cedex 4 France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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, Volume 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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