A047626 - OEIS

%I #19 May 15 2023 08:45:34

%S 1,0,1212,11584,70380,261120,776800,1989504,4398252,8878080,16788312,

%T 29833920,50078944,80686080,126457920,191702144,281524140,403691520,

%U 570110556,793005120,1074444600,1431982080,1903243680,2494537344,3204056800,4082872320,5185620120

%N Theta series of 14-dimensional integral laminated lattice LAMBDA14.3 with minimal norm 4.

%C This theta series is an element of the space of modular forms on Gamma_1(4) with Kronecker character, weight 7, and dimension 4. - _Andy Huchala_, May 15 2023

%H Andy Huchala, <a href="/A047626/b047626.txt">Table of n, a(n) for n = 0..10000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA14.3.html">Home page for this lattice</a>

%o (Magma)

%o prec := 30;

%o gram := [4,2,4,0,-2,4,0,-2,0,4,0,0,-2,0,4,-2,-2,0,0,0,4,0,0,0,0,0,-2,4,0,0,0,0,0,0,-2,4,0,0,0,0,1,-1,0,0,4,0,0,0,0,-1,0,0,0,0,4,0,0,0,0,0,0,0,0,-2,0,4,0,1,-2,0,1,0,0,-1,1,0,0,4,-1,0,-1,-1,1,0,1,0,1,1,0,0,4,-2,-1,0,0,0,1,0,-1,1,1,0,1,0,4];

%o S := SymmetricMatrix(gram);

%o L := LatticeWithGram(S);

%o T := ThetaSeriesModularForm(L);

%o Coefficients(PowerSeries(T,prec)); // _Andy Huchala_, May 15 2023

%Y Cf. A023937, A046958, A047627.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, May 15 2023