Open AccessMACKAY FUNCTIONS AND EXACT CUTTING IN SPACES OF MODULAR FORMS
Author(s) -
Галина Валентиновна Воскресенская
Publication year - 2017
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2017-23-2-15-25
Subject(s) - mathematics , modular form , pure mathematics , multiplicative function , space (punctuation) , quadratic equation , modular design , function (biology) , mathematical analysis , algebra over a field , geometry , computer science , evolutionary biology , biology , operating system
In the article we consider structure problems in the theory of modular forms. The phenomenon of the exact cutting for the spaces Sk(Γ0(N), χ), where χ is a quadratic character with the condition χ(−1) = = (−1)k . We prove that for the levels N ̸= 3, 17, 19 the cutting function is a multiplicative eta–product of an integral weight. In the article we give the table of the cutting functions. We prove that the space of an cutting function is one–dimensional. Dimensions of the spaces are calculated by the Cohen-Oesterle formula, the orders in cusps are calculated by the Biagioli formula.