  Based on the notion of strong modular form developed in Part I, we propose to
structure the family of cuspidal modular form spaces
$(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ and to determine bases for each of
these spaces, once known bases for the first values of $k$.
  We then apply these theoretical results to explicitly determine bases for
space families $(S_{2k}(\Gamma_0(N)))_{k\in \mathbb{N}^*}$ when $1\leq N \leq
10$.
