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The modular discriminant $\Delta$ is known to structure the sequence ofmodular forms $(M_{2k}(SL_2(\mathbb{Z})))_{k\in \; \mathbb{N}^*}$ at level$1$.\\ For all positive integer $N$, we define a strong modular unit $\Delta_N$at level $N$ which enables one to structure the sequence$(M_{2k}(\Gamma_0(N)))_{k\in \; \mathbb{N}^*}$ in an identical way. We willapply this result to the bases search for each of the spaces$(M_{2k}(\Gamma_0(N)))_{k\in \; \mathbb{N}^*}$.\\ This article is the first ina series of three. In the second part we will propose explicit bases of$(M_{2k}(\Gamma_0(N)))_{k\in \; \mathbb{N}^*}$ for $1\leq N \leq 10$. Finally,in a third part, we will apply the results obtained in the first two parts to$(S_{2k}(\Gamma_0(N)))_{k\in \; \mathbb{N}^*}$.

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 I : Strong modular units