  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 $(M_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$
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 $1\leq N \leq 10$.
