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A015233
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Theta series of lattice Kappa_9.
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2
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1, 0, 180, 416, 1620, 3024, 6404, 9408, 18876, 20048, 43224, 45408, 70462, 82272, 138408, 121600, 213972, 210816, 298620, 310176, 472464, 391376, 675168, 604032, 794524, 808512, 1208568, 949568, 1533048, 1361328, 1781632, 1719744, 2435580, 1916336, 3092616
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 161.
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LINKS
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EXAMPLE
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G.f. = 1 + 180*q^4 + 416*q^6 + ...
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PROG
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(Magma)
L := (Lattice("Kappa", 9));
B := Basis(ThetaSeriesModularFormSpace(L), 100);
S := [1, 0, 180, 416, 1620, 3024, 6404, 9408, 18876, 20048, 43224, 45408, 70462, 82272, 138408, 121600, 213972, 210816, 298620, 310176, 472464, 391376, 675168, 604032, 794524, 808512, 1208568, 949568, 1533048, 1361328, 1781632, 1719744, 2435580, 1916336];
Coefficients(&+[B[i] * S[i] : i in [1..34]]); // Andy Huchala, Jul 23 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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