A007258 - OEIS

A007258

McKay-Thompson series of class 6E for Monster (and, apart from signs, of class 12B).
(Formerly M4052)

1, 0, 6, 4, -3, -12, -8, 12, 30, 20, -30, -72, -46, 60, 156, 96, -117, -300, -188, 228, 552, 344, -420, -1008, -603, 732, 1770, 1048, -1245, -2976, -1776, 2088, 4908, 2900, -3420, -7992, -4658, 5460, 12756, 7408, -8583, -19944, -11564, 13344, 30756, 17744, -20448, -46944, -26916

(list; graph; refs; listen; history; text; internal format)

OFFSET

-1,3

COMMENTS

Also normalized Hauptmodul for Gamma_0(6).

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275.

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.

Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of 5 + eta(q)^5*eta(q^3)/(eta(q^2)*eta(q^6)^5) in powers of q.

EXAMPLE

T6E = 1/q + 6*q + 4*q^2 - 3*q^3 - 12*q^4 - 8*q^5 + 12*q^6 + 30*q^7 + ...

MATHEMATICA

QP = QPochhammer; s = 5*q + QP[q]^5*(QP[q^3]/(QP[q^2]*QP[q^6]^5)) + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015 *)

PROG

(PARI) q='q+O('q^30); Vec(5 +(eta(q)^5*eta(q^3))/(q*eta(q^2)*eta(q^6)^5)) \\ G. C. Greubel, May 09 2018

CROSSREFS

Essentially same as A045488.