login
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
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
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<q> := 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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 28 2005
EXTENSIONS
Name clarified and more terms from Andy Huchala, May 13 2023
STATUS
approved