A345658 Theta series of the canonical laminated lattice LAMBDA_27.

1, 0, 0, 0, 197142, 49152, 17938944, 13565952, 500022972, 549519360, 7119111168, 8746696704, 64795688552, 80374972416, 426695568384, 515432841216, 2207141692182, 2563069771776, 9461992962048

Offset

0,5

Comments

Theta series is an element of the space of modular forms on Gamma_0(16) of weight 27/2 and dimension 28 over the integers.

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 179.

Links

Table of n, a(n) for n=0..18.

J. H. Conway and N. J. A. Sloane, Laminated lattices, Annals of Math., 116 (1982), pp. 593-620. A revised version appears as Chapter 6 of "Sphere Packings, Lattices and Groups" by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.

J. H. Conway and N. J. A. Sloane, The "shower" showing containments among the laminated lattices up to dimension 48 (Fig 3 from the Annals paper, also Fig. 6.1 in the Sphere packing book).

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

Index entries for sequences related to laminated lattices

Example

G.f.: 1 + 197142*q^8 + 49152*q^10 + ...

Prog

(Magma)
L := Lattice("Lambda", 27);
T<q> := ThetaSeries(L, 14);
C := Coefficients(T);
[C[2*i-1] : i in [1..7]];

Crossrefs

Cf. A005135.

Sequence in context: A305699 A035230 A099818 * A185519 A345659 A344942

Adjacent sequences: A345655 A345656 A345657 * A345659 A345660 A345661

Keyword

nonn,more

Author

Andy Huchala, Jun 21 2021

Extensions

a(16)-a(18) from Robin Visser, Sep 24 2023

Status

approved