A003785 Coefficients of Jacobi cusp form of index 1 and weight 12.

1, 10, 0, 0, -88, -132, 0, 0, 1275, 736, 0, 0, -8040, -2880, 0, 0, 24035, 13080, 0, 0, -14136, -54120, 0, 0, -128844, 115456, 0, 0, 389520, 38016, 0, 0, -256410, -697950, 0, 0, -806520, 963160, 0, 0, 1892363, 938400, 0, 0, -1227600, -2309120, 0, 0, -813450, -2813096, 0, 0

Offset

3,2

References

M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985, p. 141.

Links

Table of n, a(n) for n=3..54.

Formula

(theta_3(z)^4+(theta_2(z)^4)/4)*eta(4z)^18*theta_4(z). - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 11 2000

a(4*n+1) = a(4*n+2) = 0.

Example

q^3 + 10*q^4 - 88*q^7 - 132*q^8 + 1275*q^11 + 736*q^12 - 8040*q^15 - ...

Prog

(PARI) {a(n) = local(A, A1); if( n<3, 0, n -= 3; A = x * O(x^n); A1 = (eta(x^2 + A)^3 / eta(x + A) / eta(x^4 + A)^2)^4 ; polcoeff( (A1 + 4 * x / A1) * eta(x^2 + A)^7 * eta(x^4 + A)^18 / eta(x + A)^2, n))} /* Michael Somos, Oct 24 2007 */

Crossrefs

Cf. A003784.

Sequence in context: A341809 A340947 A306934 * A287711 A287783 A288394

Adjacent sequences: A003782 A003783 A003784 * A003786 A003787 A003788

Keyword

sign

Author

N. J. A. Sloane, Mar 15 1996

Status

approved