V. Level 5. The McKay-Thompson series of class 5B for the Monster.
$$j_{5B}(\tau) =\left(\frac{\eta(\tau)}{\eta{(5\tau)}}\right)^{6}$$
Examples. Surprisingly, the following "cubes" are powers of the golden ratio \(\phi=\frac{1+\sqrt5}2\) $$\begin{align}j_{5B}\Big(\tfrac{1+\sqrt{-7/5}}{2}\Big) &= -(\sqrt5)^3\,\phi^3\\ j_{5B}\Big(\tfrac{1+\sqrt{-23/5}}{2}\Big) &= -(\sqrt5)^3\,\phi^9\\ j_{5B}\Big(\tfrac{1+\sqrt{-47/5}}{2}\Big) &= -(\sqrt5)^3\,\phi^{15}\end{align}$$ These discriminants \(d=5m\) have class number \(h(-d)=2\).
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