A261403 Coefficients of an example of a modular form of weight 2 for the group Gamma_0(32).

1, 12, 4, 0, 0, -24, -16, 0, -8, -36, 24, 0, 0, 72, -32, 0, 24, 24, 52, 0, 0, 0, -48, 0, -32, -12, 56, 0, 0, -120, -96, 0, 24, 0, 72, 0, 0, -24, -80, 0, -48, 120, 128, 0, 0, 72, -96, 0, 96, -84, 124, 0, 0, 168, -160, 0, -64, 0, 120, 0, 0, -120, -128, 0, 24, -144, 192, 0, 0, 0, -192

Offset: 0

Author

N. J. A. Sloane, Aug 20 2015

Keywords

• sign

Comments

This is a particular member of an eight-dimensional vector space.

Links

• Robin Visser, Table of n, a(n) for n = 0..1000
• John F. R. Duncan, Michael J. Griffin and Ken Ono, Proof of the Umbral Moonshine Conjecture, arXiv:1503.01472, 2015, See Eq. (B.88).

Crossrefs

Cf. A002171.

Programs

Sage

def a(n):
    B = ModularForms(Gamma0(32),2).basis()
    f = B[1] + 12*B[0] + 4*B[3] - 16*B[6] - 8*B[7]
    return f.coefficient(n)  # Robin Visser, Dec 12 2023

Extensions

More terms from Robin Visser, Dec 12 2023