Geodesic
Finite simple groups and multiplicative $\eta$-products
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 71-91

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In this article the author finds all such simple groups that the cusp forms associated with all elements of these groups by a faithful representation are $\eta$-products with multiplicative Fourier coefficients. Bibl. – 18 titles. 
@article{ZNSL_2010_375_a5,
     author = {G. V. Voskresenskaya},
     title = {Finite simple groups and multiplicative $\eta$-products},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {71--91},
     publisher = {mathdoc},
     volume = {375},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a5/}
}
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G. V. Voskresenskaya. Finite simple groups and multiplicative $\eta$-products. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 19, Tome 375 (2010), pp. 71-91. http://geodesic.mathdoc.fr/item/ZNSL_2010_375_a5/