

A345662


Theta series of the canonical laminated lattice LAMBDA_31.


0



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

0,5


COMMENTS

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 2.264, 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).


REFERENCES

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


LINKS

J. H. Conway and N. J. A. Sloane, Laminated lattices, Annals of Math., 116 (1982), pp. 593620. A revised version appears as Chapter 6 of "Sphere Packings, Lattices and Groups" by J. H. Conway and N. J. A. Sloane, SpringerVerlag, NY, 1988.


EXAMPLE

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


PROG

(Magma)
L := Lattice("Lambda", 31);
T<q> := ThetaSeries(L, 14);
C := Coefficients(T);
[C[2*i1] : i in [1..8]];


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



