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A107498 Theta series of quadratic form with Gram matrix [ 4, -1, 1, 1; -1, 10, 3, 3; 1, 3, 10, -3; 1, 3, -3, 88].

%I A107498 #19 May 14 2023 04:11:54
%S A107498 1,0,2,0,0,4,4,4,6,0,0,8,0,2,0,8,0,0,6,8,12,8,0,0,12,0,6,0,8,0,0,12,
%T A107498 14,8,8,0,0,4,0,8,0,16,0,0,24,16,16,24,0,0,26,0,14,0,36,0,0,20,24,28,
%U A107498 44,0,0,32,0,12,0,20,0,0,40,36,58,16,0,0,52,0,24
%N A107498 Theta series of quadratic form with Gram matrix [ 4, -1, 1, 1; -1, 10, 3, 3; 1, 3, 10, -3; 1, 3, -3, 88].
%C A107498 G.f. is theta_2 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 A107498 Andy Huchala, <a href="/A107498/b107498.txt">Table of n, a(n) for n = 0..20000</a>
%H A107498 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 A107498 G.f. = 1 + 2*q^4 + 4*q^10 + 4*q^12 + ...
%o A107498 (Magma)
%o A107498 prec := 60;
%o A107498 ls := [[4, -1, 1, 1], [-1, 10, 3, 3], [1, 3, 10, -3], [1, 3, -3, 88]];
%o A107498 S := Matrix(ls);
%o A107498 L := LatticeWithGram(S);
%o A107498 M := ThetaSeriesModularFormSpace(L);
%o A107498 B := Basis(M, prec);
%o A107498 T<q> := ThetaSeries(L, 48);
%o A107498 coeffs := [Coefficients(T)[2*i-1] : i in [1..23]];
%o A107498 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 A107498 Cf. A107497 - A107505, A140686.
%K A107498 nonn
%O A107498 0,3
%A A107498 _N. J. A. Sloane_, May 28 2005
%E A107498 Name clarified and more terms from _Andy Huchala_, May 13 2023