Thompson series is a Hauptmodul for a genus zero group which lies between $Gamma$o(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series $T_g$($alpha$) (Theorem 4), which would be an extension of [3], Theorem 3.7.5 (2) by using the Shimura theory and the standard results of complex multiplication. Also we construct various class fields over K, over a CM-field K (${zeta}N + {zeta}_N^{-1}$), and over a field K (${zeta}N$). Furthermore, we find an explicit formula for the conjugates of Tg ($alpha$) to calculate its minimal polynomial where $alpha$ (${in}{eta}$) is the quotient of a basis of an integral ideal in K.