Titlebook: Eta Products and Theta Series Identities; Günter Köhler Book 2011 Springer-Verlag Berlin Heidelberg 2011 11-02, 11F20, 11F27, 11R11.Eisens

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Liang See Tan,Keith Chiu Kian Tantions in some textbooks; we mention (Miyake in Modular Forms, Springer, Berlin, .), pp. 90–95, 182–185, (Neukirch in Algebraische Zahlentheorie, Springer, Berlin, .. English Translation: Algebraic Number Theory, Springer, Berlin, 1999), pp. 491–514. Here we will reproduce relevant definitions and results, but we will not give proofs.

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Groups of Coprime Residues in Quadratic Fieldsecifying its values on the generators. In almost all of the examples in Part II we will define characters in this way. For this purpose we need to know a decomposition of the groups into direct factors, and we need to know generators of the factors.

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The prime level ,=3oduct of level . and weight 1 for primes .≥5. The eta product .(.).(3.) is identified with a Hecke theta series for .; the result (11.2) is known from (Dummit et al. in Finite Groups—Coming of Age. Contemp. Math. 45, 89–98, .), (Köhler in Math. Z. 197, 69–96, .).