A023942 -id:A023942 - cp's OEIS frontend

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

Andy Huchala, Jun 21 2021

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.

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

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

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

Cf. A005135, A023942, A008408.

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

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

A345660 Theta series of the canonical laminated lattice LAMBDA_29.

Original entry on oeis.org

1, 0, 0, 0, 198506, 163840, 20662272, 45481984, 745402040, 1904738304, 13582315520, 32267304960, 152158214640, 321893203968, 1194291679232, 2263580016640, 7176091448362

Offset: 0

Andy Huchala, Jun 27 2021

Theta series is an element of the space of modular forms on Gamma_0(16) of weight 29/2 and dimension 30 over the integers.

			G.f.: 1 + 198506*q^8 + 163840*q^10 + ...

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

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

Cf. A005135, A023942, A008408.

L := Lattice("Lambda", 29);
T := ThetaSeries(L, 14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];

a(14)-a(16) from Robin Visser, Sep 24 2023

A345661 Theta series of the canonical laminated lattice LAMBDA_30.

Original entry on oeis.org

1, 0, 0, 0, 200046, 294912, 23779584, 82378752, 1032132696, 3570794496, 21539288064, 64122912768, 266965225878, 683889819648, 2273486860032, 5134106886144

Offset: 0

Andy Huchala, Jun 29 2021

Theta series is an element of the space of modular forms on Gamma_1(24) with Kronecker character -3 in modulus 24, weight 15, and dimension 60 over the integers.

			1 + 200046*q^8 + 294912*q^10 + ...

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

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

Cf. A005135, A023942, A008408.

L := Lattice("Lambda", 30);
T := ThetaSeries(L,14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];

a(11)-a(15) from Robin Visser, Sep 24 2023

A345662 Theta series of the canonical laminated lattice LAMBDA_31.

Original entry on oeis.org

1, 0, 0, 0, 202692, 516096, 29046528, 145195008, 1538419918, 6537101312, 36946043904, 124680077312, 511130138792, 1419643330560, 4752698632192

Offset: 0

Andy Huchala, Jun 29 2021

Theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character 8 in modulus 32, weight 31/2, and dimension 62 over the integers.

As of version 2.26-4, the largest rank of a laminated lattice which is recognized by Magma is 31, but laminated lattices of larger rank exist (see Conway and Sloane reference).

			G.f.: 1 + 202692*q^8 + 516096*q^10 + ...

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

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

Cf. A005135, A023942, A008408, A002336.

L := Lattice("Lambda", 31);
T := ThetaSeries(L,14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];

a(11)-a(14) from Robin Visser, Sep 24 2023

cp's OEIS Frontend

A345657 Theta series of the canonical laminated lattice LAMBDA_26.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Magma

Extensions

A345660 Theta series of the canonical laminated lattice LAMBDA_29.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Magma

Extensions

A345661 Theta series of the canonical laminated lattice LAMBDA_30.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Magma

Extensions

A345662 Theta series of the canonical laminated lattice LAMBDA_31.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Magma

Extensions