Open AccessON SPACES OF MODULAR FORMS OF EVEN WEIGHT
Author(s) -
G. V. Voskresenskaya
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-10-38-47
Subject(s) - modular form , mathematics , cusp form , cusp (singularity) , modulo , multiplicative function , space (punctuation) , pure mathematics , product (mathematics) , function (biology) , weight function , combinatorics , mathematical analysis , geometry , computer science , evolutionary biology , biology , operating system
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 xed 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 Sk (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.