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Complex multiplication of two eta-products. (English) Zbl 1444.11064
Summary: The $$q$$-coefficients of a Hecke eigenform possess a multiplicative property, and in addition, if it has complex multiplication, the CM structure admits an efficient method of computing all coefficients. We use Euler’s pentagonal numbers theorem and Jacobi’s triangular numbers theorem to directly prove this CM phenomenon for two eta-products $$\eta^4(6\tau)$$ and $$\eta^6(4\tau)$$.
##### MSC:
 11F20 Dedekind eta function, Dedekind sums 11F30 Fourier coefficients of automorphic forms
##### Keywords:
eta-products; Hecke eigenform
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