Cusp forms with characters of the level $\mathrm{p}$

In the article we prove structure theorems for spaces of cusp forms with characters of a level $\mathrm{p}$. The spaces are decomposed in the direct sum of three subspaces. The first subspace is essencial. The eta-quotions play an important role in the investigations. The divisor of the functions is concentrated in cusps. The theorem about the structure of spaces of modular forms with characters is proved. We discuss the question about generators of these spaces and K.Ono’s problem. Dimensions of spaces are calculated by the Cohen–Oesterle formula, the orders in cusps are calculated by the Biagioli formula.