Geodesic
Finite Groups and Families of Modular Forms Associated with Them
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 528-541

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In the paper, a correspondence between finite groups and $q$-series which, under specialization, are Fourier expansions of modular forms is studied. The categories thus arising are investigated. The problem of describing groups to which $q$-series with multiplicative coefficients correspond is considered. Subgroups of this kind are contained in any group. The notion of modular analog of the genetic code of a group is introduced and studied.
Keywords: finite group, modular form, $q$-series, Hecke operator, Dedekind $\eta$-function, group representation, Sylow subgroup.
Mots-clés : multiplicative coefficient, Fourier expansion 
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     author = {G. V. Voskresenskaya},
     title = {Finite {Groups} and {Families} of {Modular} {Forms} {Associated} with {Them}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {528--541},
     publisher = {mathdoc},
     volume = {87},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a5/}
}
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G. V. Voskresenskaya. Finite Groups and Families of Modular Forms Associated with Them. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 528-541. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a5/