Geodesic
On spaces of modular forms of even weight
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 38-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 and 19 the cutting function is a multiplicative eta – product. In the common case the space $f(z)M_{k-l}(\Gamma_0(N))$ is not equal to the space $S_k(\Gamma_0(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.
Keywords: modular forms, cusp forms, Dedekind eta-function, Eisenstein series, divisor of function, structure theorems, Cohen–Oesterle formula.
Mots-clés : parabolic vertex 
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     author = {G. V. Voskresenskaya},
     title = {On spaces of modular forms of even weight},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {38--47},
     year = {2014},
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G. V. Voskresenskaya. On spaces of modular forms of even weight. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 38-47. http://geodesic.mathdoc.fr/item/VSGU_2014_10_a3/

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