

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



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<q> := ThetaSeries(L, 48);
coeffs := [Coefficients(T)[2*i1] : 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,changed


AUTHOR



EXTENSIONS

Name clarified and more terms from Andy Huchala, May 13 2023


STATUS

approved



