Complex multiplication of two eta-products
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 7-24
MSC: Primary 11F20; Secondary 11F30.
DOI: 10.4064/cm7134-12-2018
Published online: 11 September 2019
Abstract
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 $\eta ^6(4\tau )$.
