|
%I #24 May 14 2023 09:40:05
%S 1,0,0,2,4,0,0,0,0,2,6,0,6,2,6,0,8,2,0,0,0,0,14,6,0,10,6,12,0,8,20,0,
%T 0,0,0,12,24,0,22,8,28,0,26,14,0,0,0,0,36,16,0,24,14,22,0,22,30,0,0,0,
%U 0,20,34,0,30,12,36,0,32,30,0,0,0,0,26,30,0,20
%N Theta series of quadratic form with Gram matrix [ 6, 3, 2, 2; 3, 8, 1, 1; 2, 1, 18, 5; 2, 1, 5, 44].
%C G.f. is theta_5 in the Parry 1979 reference on page 166. This theta series is an element of the space of modular forms on Gamma_0(169) of weight 2 and dimension 21. - _Andy Huchala_, May 13 2023
%H Andy Huchala, <a href="/A107501/b107501.txt">Table of n, a(n) for n = 0..20000</a>
%H W. R. Parry, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002196476">A negative result on the representation of modular forms by theta series</a>, J. Reine Angew. Math., 310 (1979), 151-170.
%e G.f. = 1 + 2*q^6 + 4*q^8 + 2*q^18 + 6*q^20 + ...
%o (Magma)
%o prec := 90;
%o ls := [[6, 3, 2, 2], [3, 8, 1, 1], [2, 1, 18, 5], [2, 1, 5, 44]];
%o S := Matrix(ls);
%o L := LatticeWithGram(S);
%o M := ThetaSeriesModularFormSpace(L);
%o B := Basis(M, prec);
%o T<q> := ThetaSeries(L, 48);
%o coeffs := [Coefficients(T)[2*i-1] : i in [1..23]];
%o Coefficients(&+[coeffs[i]*B[i] :i in [1..13]]+&+[coeffs[i+1]*B[i] :i in [14..19]] + coeffs[22]*B[20] + coeffs[23]*B[21]); // _Andy Huchala_, May 13 2023
%Y Cf. A107498, A107499, A107500, A107502, A107503, A107504, A107505.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, May 28 2005
%E Name clarified and more terms from _Andy Huchala_, May 13 2023
|
