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Theta series of laminated lattice LAMBDA_19.
2

%I #17 Sep 08 2022 08:44:48

%S 1,0,10668,317952,3747430,24569856,117503960,428990464,1355705388,

%T 3631734784,9033649880,19996626432,42549627976,82713667584,

%U 157758704304,279165280256,490745951846,808950325248,1335670719108,2081937198592,3270650346456,4874720530432

%N Theta series of laminated lattice LAMBDA_19.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 174.

%H Andy Huchala, <a href="/A023941/b023941.txt">Table of n, a(n) for n = 0..20000</a>

%e G.f.: 1 + 10668*q^4 + 317952*q^6 + 3747430*q^8 + 24569856*q^10 + 117503960*q^12 + ...

%o (Magma) L:=Lattice("Lambda",19); T<q> := ThetaSeries(L,12); T;

%o (Magma)

%o L := Lattice("Lambda",19);

%o B := Basis(ThetaSeriesModularFormSpace(L),30);

%o S := [1, 0, 10668, 317952, 3747430, 24569856, 117503960, 428990464, 1355705388, 3631734784, 9033649880, 19996626432, 42549627976, 82713667584, 157758704304, 279165280256, 490745951846, 808950325248, 1335670719108, 2081937198592];

%o Coefficients(&+[B[i] * S[i] : i in [1..20]]); // _Andy Huchala_, Jun 17 2021

%K nonn

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Andy Huchala_, Jun 17 2021