A047628 - OEIS

%I #27 May 10 2023 05:19:58

%S 1,0,1242,11916,72252,266544,807090,2006856,4603284,8924940,17571816,

%T 30168396,51799212,82147608,132245676,191541024,294596676,410924988,

%U 590219898,800792568,1123700904,1442103768,1991926080,2519984088,3314316426,4155999192,5427108108

%N Theta series of 14-dimensional lattice Kappa_{14} with minimal norm 4.

%C Theta series is an element of the space of modular forms on Gamma_1(18) with Kronecker character -3 in modulus 18, weight 7, and dimension 22 over the integers. - _Andy Huchala_, May 07 2023

%D J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chap. 6.

%H Andy Huchala, <a href="/A047628/b047628.txt">Table of n, a(n) for n = 0..20000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/KAPPA14.1.html">Home page for this lattice</a>

%o (Magma)

%o prec := 80;

%o S := SymmetricMatrix([4,2,4,0,-2,4,0,-2,0,4,0,0,-2,0,4,-2,-2,0,0,0,4,-2,-1,1,0,0,0,4,-2,-1,0,-1,1,2,2,4,-2,-2,0,1,1,2,2,2,4,-2,0,-2,0,1,1,0,0,0,4,1,1,0,0,0,-2,0,-1,-1,-2,4,-2,-1,0,0,0,1,1,1,1,1,-2,4,0,-1,1,1,0,-1,1,0,0,-1,1,-1,4,0,0,0,0,0,0,1,0,1,-1,1,-1,1,4]);

%o L := LatticeWithGram(S);

%o T<q> := ThetaSeries(L, 42);

%o M := ThetaSeriesModularFormSpace(L);

%o B := Basis(M, prec);

%o Coefficients(&+[Coefficients(T)[2*i-1]*B[i] :i in [1..22]]); // _Andy Huchala_, May 07 2023

%Y Cf. A029897, A362875, A362876, A362877, A362878, A362879, A362880.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, May 07 2023