Geodesic
Multiplicative Products of Dedekind $\eta$-Functions and Group Representations
Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 511-526

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In this paper, we findall metacyclic groups ($\langle a,b\colon a^m=e,\,b^s=e,\,b^{-1}ab=a^r\rangle$), where $m=10$, $14$, $15$, $20$, $21$, $22$, such that the cusp forms associated with all elements of these groups by an exact representation are multiplicative $\eta$-products. We also consider the correspondence between multiplicative $\eta$-products and elements of finite order in $SL(5,C)$ by the adjoint representation. 
@article{MZM_2003_73_4_a3,
     author = {G. V. Voskresenskaya},
     title = {Multiplicative {Products} of {Dedekind} $\eta${-Functions} and {Group} {Representations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {511--526},
     publisher = {mathdoc},
     volume = {73},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a3/}
}
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G. V. Voskresenskaya. Multiplicative Products of Dedekind $\eta$-Functions and Group Representations. Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 511-526. http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a3/