Geodesic
Mackay functions and exact cutting in spaces of modular forms
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2017), pp. 15-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article we consider structure problems in the theory of modular forms. The phenomenon of the exact cutting for the spaces $S_k(\Gamma_0(N),\chi),$ where $\chi$ is a quadratic character with the condition $\chi(- 1) = ( - 1)^k$. We prove that for the levels $N \ne 3,~17,~19$ 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.
Keywords: modular forms, cusp forms, Dedekind eta-function, cusps, Eisenstein series, divisor of function, structure theorems, Cohen–Oesterle formula. 
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     author = {G. V. Voskresenskaya},
     title = {Mackay functions and exact cutting in spaces of modular forms},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {15--25},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2017_2_a1/}
}
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G. V. Voskresenskaya. Mackay functions and exact cutting in spaces of modular forms. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2017), pp. 15-25. http://geodesic.mathdoc.fr/item/VSGU_2017_2_a1/

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