A006913 Theta series of laminated lattice LAMBDA_12^{mid}. (Formerly M5467)

1, 0, 632, 3328, 18440, 44032, 139872, 236032, 589576, 829440, 1803600, 2250496, 4499360, 5196800, 9676480, 10694144, 18865928, 19884032, 34147224, 34636032, 57643440, 57413632, 92796192, 90131968, 143856544, 136744960, 213841936, 201703936, 309939520

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_0(8) of weight 6 and dimension 7 over the integers. - Andy Huchala, May 10 2023

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 157.

E. C. Pervin, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Andy Huchala, Table of n, a(n) for n = 0..20000

G. Nebe and N. J. A. Sloane, Home page for this lattice

Prog

(Magma)
prec := 20;
S := SymmetricMatrix([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]);
L := LatticeWithGram(S);
T<q> := ThetaSeries(L, 12);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] : i in [1..7]]); // Andy Huchala, May 10 2023

Crossrefs

Sequence in context: A345557 A345811 A186898 * A154088 A321639 A185483

Adjacent sequences: A006910 A006911 A006912 * A006914 A006915 A006916

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Andy Huchala, May 10 2023

Status

approved