Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series

(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)

izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ

(8) = {

∈SL

(Z)│

≡()mod 8} (※Equation, See Full-text). If n

24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient

(sub)A(z)/

(sub)B(z) is a modular function for Γ

(8). Since we identify the field of modular functions for Γ

(8) with the function field K(X

(8)) of the modular curve X

(8) = Γ

(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X

(8)) and defined by j(sub)1,8(z) =

(2z)/

(4z). Here,

is the classical Jacobi theta series.