

A107502


Theta series of quadratic form with Gram matrix [ 4, 1, 0, 1; 1, 10, 0, 3; 0, 0, 26, 13; 1, 3, 13, 36].


6



1, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 2, 0, 6, 0, 0, 10, 8, 14, 12, 0, 0, 20, 0, 6, 0, 16, 0, 0, 8, 18, 18, 12, 0, 0, 12, 0, 8, 0, 6, 0, 0, 30, 22, 20, 10, 0, 0, 22, 0, 14, 0, 38, 0, 0, 22, 30, 18, 48, 0, 0, 30, 0, 12, 0, 22, 0, 0, 38, 16, 50, 30, 0, 0, 46, 0
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OFFSET

0,3


COMMENTS

G.f. is theta_6 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^4 + 2*q^10 + 2*q^12 + ...


PROG

(Magma)
prec := 90;
ls := [[4, 1, 0, 1], [1, 10, 0, 3], [0, 0, 26, 13], [1, 3, 13, 36]];
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


AUTHOR



EXTENSIONS

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


STATUS

approved



