Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University450810.18287/2541-7525-2014-20-10-38-47ON SPACES OF MODULAR FORMS OF EVEN WEIGHTVoskresenskayaG.V.morenov.sv@ssau.ruSamara State University29122014201038472905201729052017Copyright © 2014, Voskresenskaya G.2014<p>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 <sub>k-l</sub>(Γ<sub>0</sub>(N)) is not equal to the space S<sub>k</sub> (Γ<sub>0</sub>(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.</p>модулярные формыпараболические формыэта- функция Дедекиндапараболические вершиныряды Эйзенштейнадивизор функцииструктурные теоремыформула Коэна - Остерлеmodular forms, cusp forms, Dedekind eta-function, parabolic vertex, Eisenstein series, divisor of function, structure theorems, Cohen — Oesterle formula