A345657 Theta series of the canonical laminated lattice LAMBDA_26.

1, 0, 0, 0, 196848, 24576, 17356032, 6782976, 448438518, 274735104, 5823343872, 4366565376, 48362165472, 39912726528, 292010062848, 253343072256, 1393763244336, 1241347399680, 5550621292032, 5010361122816

Offset

0,5

Comments

Theta series is an element of the space of modular forms on Gamma_1(24) with Kronecker character -3 in modulus 24, weight 13, and dimension 52 over the integers.

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 178.

Links

Table of n, a(n) for n=0..19.

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

1 + 196848*q^8 + 24576*q^10 + ...

Prog

(Magma)
L := Lattice("Lambda", 26);
T<q> := ThetaSeries(L, 14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];

Crossrefs

Cf. A005135, A023942, A008408.

Sequence in context: A175744 A024211 A204943 * A113919 A001379 A247242

Adjacent sequences: A345654 A345655 A345656 * A345658 A345659 A345660

Keyword

nonn,more

Author

Andy Huchala, Jun 21 2021

Extensions

a(17)-a(19) from Robin Visser, Sep 24 2023

Status

approved