A015236 -id:A015236 - cp's OEIS frontend

A015235 Theta series of lattice Kappa_8.

1, 0, 132, 192, 828, 1152, 2796, 2880, 6828, 5376, 14904, 10944, 20772, 18432, 40224, 25920, 53964, 41472, 76452, 58176, 107784, 69504, 156816, 101376, 163284, 131328, 259032, 147072, 295200, 206208, 357480, 250560, 432780, 269568, 576072, 365184, 555804, 426240

Offset: 0

N. J. A. Sloane

nonn

			G.f. = 1 + 132*q^4 + 192*q^6 + ...

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 161.

Andy Huchala, Table of n, a(n) for n = 0..20000
G. Nebe and N. J. A. Sloane, Home page for this lattice

Cf. A015236 (K_7), A015233 (K_9), A015232 (K_10), A015229 (K_11), A004010 (K_12), A029897 (K_13), A047628 (K_14).

L = [1, 0, 132, 192, 828, 1152, 2796, 2880, 6828, 5376]
M = ModularForms(Gamma0(12),4)
bases = [.q_expansion(35) for  in M.integral_basis()]
f = sum(x*y for (x,y) in zip(bases,L)); list(f) # Andy Huchala, Jul 23 2021

More terms from Sean A. Irvine, Feb 26 2020

A029696 Theta series of 7-dimensional lattice Kappa_7*.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 22, 0, 0, 64, 0, 0, 0, 0, 40, 0, 0, 64, 44, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 240, 0, 0, 448, 0, 0, 0, 0, 112, 0, 0, 384, 480, 0, 0, 0, 0, 0, 0, 0, 220, 0, 0, 0, 450, 0, 0, 1408, 0, 0, 0, 0, 480, 0, 0, 960, 812

Offset: 0

N. J. A. Sloane

nonn

			G.f. = 1 + 2*q^12 + 22*q^16 + ...

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 161.

Sean A. Irvine, Table of n, a(n) for n = 0..1000
Sean A. Irvine, Java program (github)
G. Nebe and N. J. A. Sloane, Home page for this lattice

Cf. A015236.

L := Dual(Lattice("Kappa", 7));
B := Basis(ThetaSeriesModularFormSpace(L), 100);
S := [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 22, 0, 0, 64, 0, 0, 0, 0, 40, 64];
Coefficients(&+[B[i] * S[i] : i in [1..26]]); // Andy Huchala, Jul 24 2021

More terms from Sean A. Irvine, Mar 02 2020

cp's OEIS Frontend

A015235 Theta series of lattice Kappa_8.

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