A033699 Theta series of lattice A_2 tensor E_7 (dimension 14, determinant 8748, minimal norm 4).

1, 0, 378, 4032, 24948, 84672, 272706, 689472, 1471554, 3003840, 6041952, 9640512, 17409420, 28304640, 42284052, 64338624, 101413620, 131362560, 198388554, 275679936, 359236080, 484706880, 685716192, 805569408, 1113880362, 1430763264, 1734830244, 2189464704

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_1(6) with Kronecker character -3 in modulus 6, weight 7, and dimension 8 over the integers. - Andy Huchala, May 13 2023

Links

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

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

Example

G.f. = 1 + 378*q^4 + 4032*q^6 + ...

Prog

(Magma)
prec := 20;
ls := [[4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -2, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, -2, -2, 4, 1, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 1, 4, -2, -2, 1, 0, 0, -2, 1], [0, 0, 0, 0, 1, -2, -2, 4, 1, -2, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0, -2, 1, 4, -2, -2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -2, -2, 4, 1, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 4, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 4, 0, 0], [0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 4, -2], [0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -2, 4]];
S := Matrix(ls);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
coeffs := [1, 0, 378, 4032, 24948, 84672, 272706, 689472];
Coefficients(&+[coeffs[i]*B[i] :i in [1..8]]); // Andy Huchala, May 13 2023

Crossrefs

Sequence in context: A235761 A154078 A047632 * A235544 A325848 A248915

Adjacent sequences: A033696 A033697 A033698 * A033700 A033701 A033702

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Edited by N. J. A. Sloane Aug 31 2009 at the suggestion of R. J. Mathar

More terms from Andy Huchala, May 13 2023

Status

approved