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Theta series of lattice Kappa_9.
2

%I #13 Jul 24 2021 01:08:27

%S 1,0,180,416,1620,3024,6404,9408,18876,20048,43224,45408,70462,82272,

%T 138408,121600,213972,210816,298620,310176,472464,391376,675168,

%U 604032,794524,808512,1208568,949568,1533048,1361328,1781632,1719744,2435580,1916336,3092616

%N Theta series of lattice Kappa_9.

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

%H Andy Huchala, <a href="/A015233/b015233.txt">Table of n, a(n) for n = 0..1500</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/KAPPA9.html">Home page for this lattice</a>

%e G.f. = 1 + 180*q^4 + 416*q^6 + ...

%o (Magma)

%o L := (Lattice("Kappa", 9));

%o B := Basis(ThetaSeriesModularFormSpace(L), 100);

%o S := [1, 0, 180, 416, 1620, 3024, 6404, 9408, 18876, 20048, 43224, 45408, 70462, 82272, 138408, 121600, 213972, 210816, 298620, 310176, 472464, 391376, 675168, 604032, 794524, 808512, 1208568, 949568, 1533048, 1361328, 1781632, 1719744, 2435580, 1916336];

%o Coefficients(&+[B[i] * S[i] : i in [1..34]]); // _Andy Huchala_, Jul 23 2021

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E a(16)-a(25) from _Sean A. Irvine_, Feb 28 2020

%E More terms from _Andy Huchala_, Jul 23 2021