and i cannot for the life of me work out how to show that this holds.
gaze your eyes upon my attempt, with the in a red box because How Do You Get That and the also in a red box because How Does That Disappear
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in reply to @bark's post:
I'm having war flashbacks. It's 2007 and im falling my algebra tests.
OMG I am so happy to see other people posting modular forms on Cohost. I really need to study them properly at some point.
I think the missing n is probably a typo (!) — the text says "which is of course equal to F if Δ=1, since then g=1", but if you try to do that the summand becomes a(n) q, which is definitely not the summand for F.
For the left-hand factor, I think the trick is that F|k γ(τ) == F|k γ_1(γ_2(τ)) == F|k γ_2(τ) (from the top of page 11). Then you can do the rest of your current approach!
(This took me like an hour to figure out)