The structure of modular form: the phenomen of the section

In the article we study the structure of spaces of modular forms $S_k(\Gamma_0(N),\chi)$ and $M_k(\Gamma_0(N),\chi)$ for the levels $N$ such that for a value $k_0~$ $S_{k_0}(\Gamma_0(N),\chi)$ is a one-dimensional space generated by a multiplicative $\eta$-product.