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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 December 5 10:56 EST 2023. Contains 367589 sequences. (Running on oeis4.)