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%I #15 May 13 2023 13:27:09
%S 1,0,378,4032,24948,84672,272706,689472,1471554,3003840,6041952,
%T 9640512,17409420,28304640,42284052,64338624,101413620,131362560,
%U 198388554,275679936,359236080,484706880,685716192,805569408,1113880362,1430763264,1734830244,2189464704
%N Theta series of lattice A_2 tensor E_7 (dimension 14, determinant 8748, minimal norm 4).
%C 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
%H Andy Huchala, <a href="/A033699/b033699.txt">Table of n, a(n) for n = 0..20000</a>
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/P14.3.html">Home page for this lattice</a>
%e G.f. = 1 + 378*q^4 + 4032*q^6 + ...
%o (Magma)
%o prec := 20;
%o 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]];
%o S := Matrix(ls);
%o L := LatticeWithGram(S);
%o M := ThetaSeriesModularFormSpace(L);
%o B := Basis(M,prec);
%o coeffs := [1, 0, 378, 4032, 24948, 84672, 272706, 689472];
%o Coefficients(&+[coeffs[i]*B[i] :i in [1..8]]); // _Andy Huchala_, May 13 2023
%K nonn
%O 0,3
%A _N. J. A. Sloane_.
%E Edited by _N. J. A. Sloane_ Aug 31 2009 at the suggestion of _R. J. Mathar_
%E More terms from _Andy Huchala_, May 13 2023
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