OFFSET
0,3
COMMENTS
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
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^4 + 4*q^10 + 4*q^12 + ...
PROG
(Magma)
prec := 60;
ls := [[4, -1, 1, 1], [-1, 10, 3, 3], [1, 3, 10, -3], [1, 3, -3, 88]];
S := Matrix(ls);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
T<q> := 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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 28 2005
EXTENSIONS
Name clarified and more terms from Andy Huchala, May 13 2023
STATUS
approved