ON SPACES OF MODULAR FORMS OF EVEN WEIGHT

In the article we study the structure of space of cusp forms of an even weight and a level N with the help of cusp forms of minimal weight of the same level. The exact cutting is studied when each cusp form is a product of fixed function and a modular form of a smaller weight. Except the levels 17 and19 the cutting function is a multiplicative eta - product. In the common case the space f(z) M _k-l(Γ₀(N)) is not equal to the space S_k (Γ₀(N)), the structure of additional space is competely studied. The result is depended on the value of the level modulo 12. Dimensions of spaces are calculated by the Cohen - Oesterle formula, the orders in cusps are calculated by the Biagioli formula.