TITLE: A Coincidence concerning 163 and the Monster?
QUESTION [6 upvotes]: There is a McKay-Thompson series for the Monster group, namely $T_{1A}$, responsible for,
$e^{\pi\sqrt{163}} \approx 640320^3 + 744$
Another one ($T_{2A}$) for,
$e^{\pi/2\sqrt{232}} \approx 396^4 -104$
And a third one ($T_{3A}$) for,
$e^{\pi/3\sqrt{267}} \approx 300^3 + 42$
It turns out, as proven by Conway, Norton, and Atkin, that this family of functions span a linear space of dimension 163.  I found this so intriguing I had to write an article on it. See,
"The 163 Dimensions of the Moonshine Functions"
The Monster is the largest of the sporadic simple groups, and 163 is the largest d such that $Q(\sqrt{-d})$ has unique factorization. Do you think this is just a coincidence?

REPLY [2 votes]: Gukov-Vafa Comm Math Phys 246, pp 181-110 has a remark in section 5.4 page 198.
I am following this up. It seems a knowledge (at least for physicists) of Ishibashi states and the Narain momentum lattice may be helpful.
Work by Connes, Consani, Marcolli, Ramachandran relates quantum statistical mechanics and class field theory.