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A107504 Theta series of quadratic form with Gram matrix [ 12, -1, 5, 2; -1, 12, 5, 2; 5, 5, 14, 3; 2, 2, 3, 22].

%I A107504 #11 May 15 2023 08:47:12
%S A107504 1,0,0,0,0,0,4,2,6,0,0,4,0,2,0,6,0,0,12,6,14,6,0,0,16,0,6,0,18,0,0,14,
%T A107504 14,10,16,0,0,10,0,8,0,18,0,0,22,26,22,12,0,0,28,0,14,0,34,0,0,24,26,
%U A107504 18,50,0,0,34,0,12,0,12,0,0,40,16,56,24,0,0,36
%N A107504 Theta series of quadratic form with Gram matrix [ 12, -1, 5, 2; -1, 12, 5, 2; 5, 5, 14, 3; 2, 2, 3, 22].
%C A107504 G.f. is theta_8 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 14 2023
%H A107504 Andy Huchala, <a href="/A107504/b107504.txt">Table of n, a(n) for n = 0..20000</a>
%H A107504 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 A107504 G.f. = 1 + 4*q^12 + 2*q^14 + 6*q^16 + ...
%o A107504 (Magma)
%o A107504 prec := 90;
%o A107504 ls := [[12, -1, 5, 2], [-1, 12, 5, 2], [5, 5, 14, 3], [2, 2, 3, 22]];
%o A107504 S := Matrix(ls);
%o A107504 L := LatticeWithGram(S);
%o A107504 M := ThetaSeriesModularFormSpace(L);
%o A107504 B := Basis(M, prec);
%o A107504 T<q> := ThetaSeries(L, 48);
%o A107504 coeffs := [Coefficients(T)[2*i-1] : i in [1..23]];
%o A107504 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 14 2023
%Y A107504 Cf. A107498-A107503, A107505.
%K A107504 nonn
%O A107504 0,7
%A A107504 _N. J. A. Sloane_, May 28 2005
%E A107504 Name clarified and more terms from _Andy Huchala_, May 14 2023