Eta product for mf.8.3.3.a (awaiting review)

This cusp form has an eta product $\eta(z)^2\eta(2z)\eta(4z)\eta(8z)^2=q\prod_{n=1}^\infty (1-q^n)^2(1-q^{2n})(1-q^{4n})(1-q^{8n})^2$, where $q=\exp(2\pi i z)$.