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 A107499 Theta series of quadratic form with Gram matrix [ 6, 2, 2, 1; 2, 18, 5, 9; 2, 5, 18, 9; 1, 9, 9, 24]. 6
 1, 0, 0, 2, 0, 0, 0, 0, 0, 4, 4, 0, 8, 2, 10, 0, 10, 8, 0, 0, 0, 0, 8, 6, 0, 12, 6, 8, 0, 4, 22, 0, 0, 0, 0, 18, 32, 0, 10, 8, 22, 0, 26, 12, 0, 0, 0, 0, 36, 18, 0, 20, 14, 16, 0, 20, 34, 0, 0, 0, 0, 10, 22, 0, 42, 12, 42, 0, 44, 26, 0, 0, 0, 0, 38, 34, 0, 30 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS G.f. is theta_3 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 LINKS Andy Huchala, Table of n, a(n) for n = 0..20000 W. R. Parry, A negative result on the representation of modular forms by theta series, J. Reine Angew. Math., 310 (1979), 151-170. EXAMPLE G.f. = 1 + 2*q^6 + 4*q^18 + 4*q^20 + ... PROG (Magma) prec := 90; ls := [[6, 2, 2, 1], [2, 18, 5, 9], [2, 5, 18, 9], [1, 9, 9, 24]]; S := Matrix(ls); L := LatticeWithGram(S); M := ThetaSeriesModularFormSpace(L); B := Basis(M, prec); T := ThetaSeries(L, 48); coeffs := [Coefficients(T)[2*i-1] : i in [1..23]]; 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 CROSSREFS Cf. A107498, A107500, A107501, A107502, A107503, A107504, A107505. Sequence in context: A005888 A213902 A170770 * A123298 A189877 A189868 Adjacent sequences: A107496 A107497 A107498 * A107500 A107501 A107502 KEYWORD nonn,changed AUTHOR N. J. A. Sloane, May 28 2005 EXTENSIONS Name clarified and more terms from Andy Huchala, May 13 2023 STATUS approved

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Last modified May 27 22:07 EDT 2023. Contains 362990 sequences. (Running on oeis4.)