A261403 - OEIS

%I #13 Dec 12 2023 08:19:25

%S 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,

%T -12,56,0,0,-120,-96,0,24,0,72,0,0,-24,-80,0,-48,120,128,0,0,72,-96,0,

%U 96,-84,124,0,0,168,-160,0,-64,0,120,0,0,-120,-128,0,24,-144,192,0,0,0,-192

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

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

%H Robin Visser, <a href="/A261403/b261403.txt">Table of n, a(n) for n = 0..1000</a>

%H John F. R. Duncan, Michael J. Griffin and Ken Ono, <a href="http://arxiv.org/abs/1503.01472">Proof of the Umbral Moonshine Conjecture</a>, arXiv:1503.01472, 2015, See Eq. (B.88).

%o (Sage)

%o def a(n):

%o     B = ModularForms(Gamma0(32),2).basis()

%o     f = B[1] + 12*B[0] + 4*B[3] - 16*B[6] - 8*B[7]

%o     return f.coefficient(n)  # _Robin Visser_, Dec 12 2023

%Y Cf. A002171.

%K sign

%O 0,2

%A _N. J. A. Sloane_, Aug 20 2015

%E More terms from _Robin Visser_, Dec 12 2023