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Thursday, October 31, 2019

Entry 54

Define dk=η(kτ) with Dedekind eta function η(τ). Then for Level 36,
(d2d23d212d18d1d4d26d9d36)2+1=(d3d12d26)2(d22d218d1d4d9d36)3(d2d23d212d18d1d4d26d9d36)23=(d26d3d12)2(d1d4d126d9d36(d2d3d12d18)4)
Or more simply a+1=ba3=c
and we find (a,b,c) as the McKay-Thompson series of class 36A for Monster (A227585). They obey,
a3a2=bca=(d26d3d12)8
(16abc+bca)+2a=abc+bca+acb
but this is not one of the 9 linear dependencies by Conway et al.

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