Geodesic
MacKay functions in spaces of higher levels
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 4, pp. 13-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article we prove structure theorems for spaces of cusps forms with the levels that are divisible by the minimal levels for MakKay functions. There are 28 eta–products with multiplicative Fourier coefficients. They are called MacKay functions. Let $f(z)$ be such function. It belongs to the space $S_l(\Gamma_0(N),\chi)$ for a minimal level $N.$ In each space of the level $N$ there is the exact cutting by the function $f(z).$ Also the function $f(z)$ is a cusp form for multiple levels. In this case the exact cutting doesn't take place and the additional spaces exist. In this article we find the conditions for the divisor of functions that are divisible by $f(z)$ and we study the structure of additional spaces. 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, structure theorems, Cohen–Oesterle formula Biagioli formula. 
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     author = {G. V. Voskresenskaya},
     title = {MacKay functions in spaces of higher levels},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {13--18},
     year = {2018},
     volume = {24},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_4_a1/}
}
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G. V. Voskresenskaya. MacKay functions in spaces of higher levels. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 4, pp. 13-18. http://geodesic.mathdoc.fr/item/VSGU_2018_24_4_a1/

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