TITLE: Why do these two Monster-related calculations yield $163$?
QUESTION [17 upvotes]: Fact 1: (1979, Conway and Norton)$^{1}$
"There are $194-22-9=\color{blue}{163\,}$ $\mathbb{Z}$-independent McKay-Thompson series for the Monster."
Note: There are  194 (linear) irreducible representations of $\mathbb{M}$, hence 194 conjugacy classes. Of these, there are 22 that are complex quadratic valued. Of the remaining, there are 9 linear dependencies.$^{2}$

Fact 2: (2004, C. Cummins)$^{3}$
"The genus 0 moonshine groups have $132 + 1 + 4 + 5  + 13 + 1  + 7=\color{blue}{163}$ equivalence classes with period 1."
Note: There are exactly $6486$ genus $0$ moonshine groups, but only $371$ equivalence classes. Of these, $310\,$ have a rational representative. (Curiously, $\color{red}{310} =163+67+43+19+11+7$.)
\begin{array}{|c|r|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{Period}& & 15^* & 11^*& 7^*& 3^*& 2^*& i& i\,2& 2 & 5 &\color{brown}{\text{Total}}\\
\hline
1&132& 0& 1& 4& 5& 0& 13& 1& 0& 7 & \color{blue}{163}\\
2&120& 0& 0& 2& 1& 7& 4& 2& 2& 2& 140\\
3& 26& 1& 0& 1& 4& 0& 2& 0& 0& 0& 34\\
4& 16& 0& 0& 0& 0& 2& 0& 0& 0& 0& 18\\
6& 10& 0& 0& 0& 0& 0& 0& 0& 0& 0& 10\\
8& 3& 0& 0& 0& 0& 0& 0& 0& 0& 0& 3\\
12& 2& 0& 0& 0& 0& 0& 0& 0& 0& 0& 2\\
24& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1\\
\hline
\color{brown}{\text{Total}}&\color{red}{310}& 1& 1& 7& 10& 9& 19& 3& 2& 9& \color{brown}{371}\\
\hline
\end{array}

Question: While the value $163$ was calculated differently in Facts 1 and 2, are they just different ways of saying the same thing, and that one implies the other? 

References:

Monstrous Moonshine, by J.H. Conway & S.P. Norton. 
Sporadic and Exceptional, by Yang-Hui He & John McKay.
Congruence Subgroups of Groups Commensurable with PSL (2, Z) of Genus 0 and 1, by C. J. Cummins. 
Tables by C. J. Cummins.

REPLY [8 votes]: If there is a connection, I would expect it to be related to the fact that the $j$ invariant is connected to both Moonshine and to class field theory.  Note that 7, 11, 19, 43, 67, and 163 are all the absolute values of  odd discriminants with class number 1.  (Strangely, 3 is missing from the list!  Otherwise the list is complete.)