A054891 Cusp form of weight 13/2 associated to the unique cusp form of weight 12 under Shimura correspondence.

1, 0, 0, -56, 120, 0, 0, -240, 9, 0, 0, 1440, -1320, 0, 0, -704, -240, 0, 0, 960, 5040, 0, 0, -12960, 1705, 0, 0, 13440, -3960, 0, 0, 5760, -6480, 0, 0, -504, -23880, 0, 0, 23520, 16320, 0, 0, -43680, 59400, 0, 0, -34560, -33551, 0, 0, -10560, 4200, 0, 0, 87360, 65520, 0, 0, -51840, -141240

Offset

1,4

References

W. Kohnen and D. Zagier, Values of L-series of modular forms at the center of the critical strip. Inv Math. 64 (1981) 175-198

Links

Table of n, a(n) for n=1..61.

Formula

See page 177 of reference. Also given by [theta_3(z)^4-(theta_2(z)^4)/8]*theta_3(z)*[(theta_2(z)*theta_4(z))^4]/16.

Prog

(PARI) {a(n) = local( A, t, T, U); if( n<0, 0, A = x * O(x^n); t = sum( k= 1, sqrtint( n), 2 * x^k^2, 1 + A); T = t^4; U = sum( k= 1, sqrtint( n), 2 * (-1)^k * x^k^2, 1 + A)^4; polcoeff( (7*T + U)/8 * (T - U)/16 * U * t, n))}

Crossrefs

Cf. A000594, A192732.

Sequence in context: A063347 A219807 A219458 * A118161 A047779 A044243

Adjacent sequences: A054888 A054889 A054890 * A054892 A054893 A054894

Keyword

sign

Author

Kok seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 23 2000

Status

approved