A159584 Coefficients in expansion of eta(2z)^3*eta(6z)^3/theta(3z).

1, 0, -3, -2, 0, 6, 6, 0, -3, -12, 0, 6, 0, 0, -6, 4, 0, 0, 6, 0, 0, 12, 0, -12, 1, 0, 9, -12, 0, -12, -30, 0, 12, 24, 0, 6, 0, 0, 24, 24, 0, -12, -18, 0, 0, -24, 0, -12, -23, 0, 6, 0, 0, -18, 48, 0, -12, 36, 0, 12, 0, 0, -18

Offset

1,3

Comments

Expansion of eta(q^2)^3*eta(q^3)^2*eta(q^12)^2/eta(q^6)^2 in powers of q.

Unique cusp form of weight 5/2, level 12 and trivial character.

Links

Table of n, a(n) for n=1..63.

G. Shimura, On modular forms of half integral weight, Annals of Math. 97 (1973) 440-481.

Example

q - 3*q^3 - 2*q^4 + 6*q^6 + 6*q^7 - 3*q^9 - 12*q^10 + ...

Prog

(Magma) Basis(CuspidalSubspace(HalfIntegralWeightForms(12, 5/2)), 64)

Crossrefs

Cf. A029769

Sequence in context: A216395 A058096 A049780 * A257653 A246834 A319730

Adjacent sequences: A159581 A159582 A159583 * A159585 A159586 A159587

Keyword

sign

Author

Steven Finch, Apr 16 2009

Status

approved