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

%I #21 May 15 2023 08:45:38

%S 1,0,1210,11552,71192,254656,804528,1915328,4538956,8628864,17309892,

%T 28803296,51649344,78486464,130311456,185010752,290432044,392591488,

%U 587974442,765028512,1108040944,1392702208,1962884944,2407505728,3303637472,3970663680,5347655844

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

%C This theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character -4 in modulus 32, weight 7, and dimension 28. - _Andy Huchala_, May 15 2023

%H Andy Huchala, <a href="/A047627/b047627.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/LAMBDA14.4.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,-1,0,-1,0,0,0,1,0,-1,0,1,1,1,4];

%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, A047626.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, May 15 2023