A056948 Jacobi form of weight 12 and index 1 associated with a nonexistent Niemeier lattice of Coxeter number 1.

1, 0, 0, -2, 26, 0, 0, 32560, 130812, 0, 0, 3671562, 9174424, 0, 0, 95675472, 188233758, 0, 0, 1142977594, 1959731160, 0, 0, 8506658544, 13293118872, 0, 0, 45762829976, 67073331776, 0, 0, 195388726752, 272567835540, 0, 0, 698077270836, 938806082418, 0, 0, 2176652437872

Offset: 0

Author

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 17 2000

Keywords

• sign

Comments

a(3) < 0 (apparently the only negative term) so the lattice cannot exist.

a(4n) + 2*Sum_{r=1..floor(sqrt(4n))} a(4*n - r^2) = A056947(n).

References

• Eichler and Zagier, The Theory of Jacobi Forms, Birkhauser 1985

Crossrefs

Cf. A003785, A055747, A056947.

Formula

E_8 * E_{4, 1} + (2*h - 60) * E_{12, 1} where h = 1.

a(n) = A055747(n) - 58*A003785(n). - Sean A. Irvine, May 18 2022