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A033699 Theta series of lattice A_2 tensor E_7 (dimension 14, determinant 8748, minimal norm 4). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 29 13:35 EDT 2024. Contains 375517 sequences. (Running on oeis4.)