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 A107497 Theta series of quadratic form with Gram matrix [ 2, 1, 1, 1; 1, 20, 7, 7; 1, 7, 20, 7; 1, 7, 7, 46]. 3
 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 8, 0, 8, 2, 4, 0, 10, 4, 0, 0, 0, 0, 12, 4, 0, 6, 6, 12, 0, 8, 20, 0, 0, 0, 0, 16, 22, 0, 24, 8, 24, 0, 32, 20, 0, 0, 0, 0, 36, 14, 0, 20, 14, 16, 0, 24, 32, 0, 0, 0, 0, 20, 28, 0, 30, 12, 44, 0, 24, 24, 0, 0, 0, 0, 28, 44, 0, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS G.f. is theta_1 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^2 + 2*q^8 + 2*q^18 + ... PROG (Magma) prec := 60; ls := [[2, 1, 1, 1], [1, 20, 7, 7], [1, 7, 20, 7], [1, 7, 7, 46]]; S := Matrix(ls); L := LatticeWithGram(S); M := ThetaSeriesModularFormSpace(L); B := Basis(M, prec); T := ThetaSeries(L, 44); 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-A107505, A140686. Sequence in context: A107494 A079205 A317641 * A000095 A258322 A258034 Adjacent sequences: A107494 A107495 A107496 * A107498 A107499 A107500 KEYWORD nonn 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 31 17:17 EDT 2023. Contains 363068 sequences. (Running on oeis4.)