A212312 4 times coefficients of the twisted K3 elliptic genus attached to the conjugacy class 7A or 7B (7AB) in the Mathieu group M_24.

-1, 213, 4767, 52682, 627573, 4682412, 53313931, 341278995, 3421674678, 24687536097, 214728131688, 1291490582217, 14602976386348, 80718169058895, 691486905294549, 5191979939244635, 44020035323951778, 245857487857551822, 2489942402834854279, 13633673140696254618

Offset: 1

Author

Charles R Greathouse IV and John F. R. Duncan, Aug 02 2012

Keywords

• sign

Links

• Miranda C. N. Cheng and John F. R. Duncan, On Rademacher sums, the largest Mathieu group, and the holographic modularity of moonshine, arXiv:1110.3859 [math.RT], 2011.
• Miranda C. N. Cheng and John F. R. Duncan, The largest Mathieu group and (mock) automorphic forms, arXiv:1201.4140 [math.RT], 2012.
• Tohru Eguchi and Kazuhiro Hikami, Note on Twisted Elliptic Genus of K3 Surface, arXiv:1008.4924 [hep-th], 2010.

Crossrefs

Other conjugacy classes: A212301-A212320.

Programs

PARI

F22(q, prec)={
    sum(s=1,min(prec-1,sqrt(2*prec)-1/2),
        my(t=0);
        forstep(r=s+1,2*prec\s,2,
            t+=(-1)^r*q^(r*s/2)
        );
        s*t
    )
};
list(n)={
    my(q='q+O('q^(n+1)),e=eta(q),f=F22(q,n),ser);
    ser=(6*sum(k=1, n, k*q^k/(1-q^k))+6*f-7*q*log(eta(7*q)/e)'-1/4)/e^3;
    Vec(4*ser)
};