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A107503 Theta series of quadratic form with Gram matrix [ 8, 1, 1, -1; 1, 18, 5, 8; 1, 5, 18, 8; -1, 8, 8, 18].

%I A107503 #16 May 14 2023 09:39:56
%S A107503 1,0,0,0,2,0,0,0,0,6,4,0,10,2,6,0,8,6,0,0,0,0,8,10,0,6,6,14,0,14,20,0,
%T A107503 0,0,0,10,24,0,16,8,28,0,28,8,0,0,0,0,34,16,0,18,14,8,0,18,40,0,0,0,0,
%U A107503 22,26,0,40,12,44,0,38,28,0,0,0,0,36,38,0,30
%N A107503 Theta series of quadratic form with Gram matrix [ 8, 1, 1, -1; 1, 18, 5, 8; 1, 5, 18, 8; -1, 8, 8, 18].
%C A107503 G.f. is theta_7 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 A107503 Andy Huchala, <a href="/A107503/b107503.txt">Table of n, a(n) for n = 0..20000</a>
%H A107503 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 A107503 G.f. = 1 + 2*q^8 + 6*q^18 + 4*q^20 + ...
%o A107503 (Magma)
%o A107503 prec := 90;
%o A107503 ls := [[8, 1, 1, -1], [1, 18, 5, 8], [1, 5, 18, 8], [-1, 8, 8, 18]];
%o A107503 S := Matrix(ls);
%o A107503 L := LatticeWithGram(S);
%o A107503 M := ThetaSeriesModularFormSpace(L);
%o A107503 B := Basis(M, prec);
%o A107503 T<q> := ThetaSeries(L, 48);
%o A107503 coeffs := [Coefficients(T)[2*i-1] : i in [1..23]];
%o A107503 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 A107503 Cf. A107498, A107499, A107500, A107501, A107502, A107504, A107505.
%K A107503 nonn
%O A107503 0,5
%A A107503 _N. J. A. Sloane_, May 28 2005
%E A107503 Name clarified and more terms from _Andy Huchala_, May 13 2023