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A107502 Theta series of quadratic form with Gram matrix [ 4, 1, 0, -1; 1, 10, 0, 3; 0, 0, 26, 13; -1, 3, 13, 36]. 6

%I #18 May 14 2023 09:39:59

%S 1,0,2,0,0,2,2,0,4,0,0,2,0,2,0,6,0,0,10,8,14,12,0,0,20,0,6,0,16,0,0,8,

%T 18,18,12,0,0,12,0,8,0,6,0,0,30,22,20,10,0,0,22,0,14,0,38,0,0,22,30,

%U 18,48,0,0,30,0,12,0,22,0,0,38,16,50,30,0,0,46,0

%N Theta series of quadratic form with Gram matrix [ 4, 1, 0, -1; 1, 10, 0, 3; 0, 0, 26, 13; -1, 3, 13, 36].

%C G.f. is theta_6 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="/A107502/b107502.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^4 + 2*q^10 + 2*q^12 + ...

%o (Magma)

%o prec := 90;

%o ls := [[4, 1, 0, -1], [1, 10, 0, 3], [0, 0, 26, 13], [-1, 3, 13, 36]];

%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, A107501, A107503, A107504, A107505.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, May 28 2005

%E Name clarified and more terms from _Andy Huchala_, May 13 2023

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Last modified July 13 15:41 EDT 2024. Contains 374284 sequences. (Running on oeis4.)