I am trying to do some experimentation with the values of Thompson series, but I have having a hard time finding a table that has these Thompson series with as many terms as I'd like. The tables I've seen only give me the required head character values up to the $q^{10}$ term.


Can someone point me to a resource that either has more terms, or (even better), a resource that might help me compute them myself in sage?


Thanks a lot for any help.



Computing Thompson series for the monster group
From MathSciNet:


MR1037906 (90m:11065) Reviewed 
McKay, John(3-CONC); Strauss, Hubertus(3-CONC)
The q-series of monstrous moonshine and the decomposition of the head characters. 
Comm. Algebra 18 (1990), no. 1, 253–278. 
11F22 (20C15 20D08 33A99) 


The authors tabulate the first fifty coefficients of the q-expansions of the Hauptmoduln which arise in the Monster-modular connection, and provide the decompositions of the corresponding Monster characters into irreducibles. This work to some extent duplicates earlier computations of S. D. Smith [in Finite groups—coming of age (Montreal, PQ, 1982), 303–313, Contemp. Math., 45, Amer. Math. Soc., Providence, RI, 1985; MR0822245 (87h:20037)] but the calculations are based on different methods which are also briefly discussed. The authors observe a surprising periodicity of the signs of the q-coefficients, a phenomenon which as yet remains unexplained.


