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I need to compute the power series of $g^2(z) + (\theta^4(z))^2$, where

$$g(z) := \frac{\eta^5(5z)}{\eta(z)},$$ where $\eta$ is the dedekind eta-function and $$\theta(z) = \sum_{n=0}^\infty q^{n^2}.$$ I am using the online Version and ChatGPT is only giving errors...