Let f be a positive definite integral ternary quadratic form and let θ(z,f)= ∑∞n=0 a(n; f)qn be its theta function.For any fixed square-free positive integer t with a(t; f)≠ 0,we define ρ(n; t,f):= a(tn2; f)/a(t; f).In the case when f = x21+x22+x23 and t = 1,Hurwitz proved that ρ(n; t,f)is multiplicative with an explicit expression.Cooper and Lam proved four similar formulas and proposed a conjecture for some other cases.By considering the action of the Hecke operaotrs on theta functions,we verify the multiplicative property of ρ(n; t,f)for many new cases,including those conjectured by Cooper and Lam.This is a joint work with Hourong Qin.