2018/08/30 by Feauveau, Jean-Christophe
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1808.10357
The modular discriminant Δ is known to structure the sequence of modular forms (M2k(SL2(ℤ)))k∈ ℕ^* at level 1. For all positive integer N, we define a strong modular unit ΔN at level N which enables one to structure the sequence (M2k(Γ0(N)))k∈ ℕ^* in an identical way. We will apply this result to the bases search for each of the spaces (M2k(Γ0(N)))k∈ ℕ^*. This article is the first in a series of three. In the second part we will propose explicit bases of (M2k(Γ0(N)))k∈ ℕ^* for 1≤ N ≤ 10. Finally, in a third part, we will apply the results obtained in the first two parts to (S2k(Γ0(N)))k∈ ℕ^*.