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 \(\eta^6(4\tau)\).