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 A029897 Theta series of 13-dimensional lattice Kappa_13 with minimal norm 4. 9

%I #10 Jul 24 2021 01:08:31

%S 1,0,918,6624,36450,120096,322436,764640,1637766,2912544,5591592,

%T 9160992,14668002,22913280,35544420,48529440,74114514,100230912,

%U 136486530,184801824,252809100,308852640,426995388,528491520,664053284,836215488,1070501400,1229873472

%N Theta series of 13-dimensional lattice Kappa_13 with minimal norm 4.

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

%H Andy Huchala, <a href="/A029897/b029897.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/KAPPA13.html">Home page for this lattice</a>

%e G.f. = 1 + 918*q^4 + 6624*q^6 + ...

%o (Magma)

%o L := (Lattice("Kappa", 13));

%o B := Basis(ThetaSeriesModularFormSpace(L), 55);

%o S := [1, 0, 918, 6624, 36450, 120096, 322436, 764640, 1637766, 2912544, 5591592, 9160992, 14668002, 22913280, 35544420, 48529440, 74114514, 100230912, 136486530, 184801824, 252809100, 308852640, 426995388, 528491520, 664053284];

%o Coefficients(&+[B[i] * S[i] : i in [1..25]]); // _Andy Huchala_, Jul 23 2021

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, Jul 23 2021

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Last modified September 15 08:13 EDT 2024. Contains 375932 sequences. (Running on oeis4.)