Eta product for mf.4.5.3.a (awaiting review)

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