A362877 - OEIS

%I #15 May 10 2023 05:19:38

%S 1,0,4266,81792,737862,3809280,15406210,47505792,133390290,312588288,

%T 711232812,1408787328,2789963820,4931371008,8870944884,14417119872,

%U 24144502662,36878456832,58393537998,84926534016

%N Theta series of 17-dimensional lattice Kappa_17.

%C Theta series is an element of the space of modular forms on Gamma_1(48) with Kronecker character 12 in modulus 48, weight 17/2, and dimension 66 over the integers.

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

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/KAPPA17.1.html">Home page for this lattice</a>.

%e G.f. = 1 + 4266*q^4 + 81792*q^6 + ...

%o (Magma)

%o prec := 10;

%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,-1,1,4,0,0,0,0,-1,1,-1,0,0,0,-1,0,0,-1,4,-1,0,0,-1,0,0,0,0,0,1,-1,1,0,0,-1,4,0,0,0,0,0,0,0,1,0,-1,1,-1,1,0,1,-1,4]);

%o L := LatticeWithGram(S);

%o T<q> := ThetaSeries(L, 2*prec);

%o [Coefficients(T)[2*i-1] : i in [1..prec]];

%Y Cf. A029897, A047628, A362875, A362876, A362878, A362879, A362880.

%K nonn

%O 0,3

%A _Andy Huchala_, May 07 2023