Editing Conway group (section)

==Generalized Monstrous Moonshine==

Conway and Norton suggested in their 1979 paper that [[monstrous moonshine]] is not limited to the monster. Larissa Queen and others subsequently found that one can construct the expansions of many Hauptmoduln from simple combinations of dimensions of sporadic groups.  For the Conway groups, the relevant McKay–Thompson series is <math>T_{2A}(\tau)</math> = {1, 0, 276, {{val|fmt=commas|−2048}}, {{val|fmt=commas|11202}}, {{val|fmt=commas|−49152}}, ...} ({{OEIS2C|id=A007246}}) and <math>T_{4A}(\tau)</math> = {1, 0, 276, {{val|fmt=commas|2048}}, {{val|fmt=commas|11202}}, {{val|fmt=commas|49152}}, ...} ({{OEIS2C|id=A097340}}) where one can set the constant term {{nowrap|1=a(0) = 24}},

:<math>\begin{align}
  j_{4A}(\tau)
    &= T_{4A}(\tau) + 24 \\
    &= \left(\frac{\eta^2(2\tau)}{\eta(\tau)\,\eta(4\tau)}\right)^{24} \\
    &= \left(\left(\frac{\eta(\tau)}{\eta(4\tau)}\right)^4 + 4^2 \left(\frac{\eta(4\tau)}{\eta(\tau)}\right)^4\right)^2 \\
    &= \frac{1}{q} + 24 + 276q + 2048q^2 + 11202q^3 + 49152q^4 + \dots
\end{align}</math>

and ''η''(''τ'') is the [[Dedekind eta function]].