Electric charge operator in the $SU(3)_{C} times SU(3)_{L} times U(1)_{X}$ model

The 3-3-1 extension of the Standard Model of the strong and electroweak interactions, with gauge group $SU(3)_{C} times SU(3)_{L} times U(1)_{X}$, provides an attempt to answer the question on family replication. There are several versions of the 3-3-1 models. In one of them, three $SU(3)_L$ lepton triplets are of the form ($nu_l, l, nu_l^c)_L$, where $nu_l^c$ is related to the right-handed component of the neutrino field $nu_l$. The particle content of this model is given as follows:
begin{equation}
psi_{iL} = left( begin{array}{c} nu_i e_i nu_i^c end{array} right)_L sim left( 3, -frac{1}{3} right), e_{iR} sim left( 1, -1 right) , i = 1, 2, 3 tag{1}
end{equation}
begin{equation}
Q_{1L} = left( begin{array}{c} u_1 d_1 U end{array} right)_L sim left( 3, frac{1}{3} right), Q_{alpha L} = left( begin{array}{c} d_alpha -u_alpha D_alpha end{array} right)_L sim left( 3^*, 0 right), alpha = 2, 3 tag{2}
end{equation}
begin{equation}
u_{iR} sim left( 1, frac{2}{3} right), d_{iR} sim left( 1, -frac{1}{3} right), U_{R} sim left( 1, frac{2}{3} right), D_{alpha R} sim left( 1, -frac{1}{3} right). tag{3}
end{equation}
Here, the values in the parentheses denote quantum numbers based on the $left( SU(3)_L, U(1)_X right)$ symmetry. $U$ and $D_alpha$ are exotic quarks whose electric charges are the same as of the usual quarks, i.e. $q_U = frac{2}{3}$ and $q_{D_alpha} = -frac{1}{3}$. In this case, the electric charge operator takes the form
begin{equation}
Q = T_{3} -frac{1}{sqrt{3}}T_8 + X tag{4}
end{equation}
where $T_a (a = 1, 2, …, 8)$ and $X$ stand for $SU(3)_L$ and $U(1)_X$ charges respectively. This paper just lists eq. (4) but does not derive it. I wonder how eq. (4) comes about? Why does the electric charge operator take this form? Besides, I am not very familiar with the $SU(3)_L$ charges. What are the values of $T_a$ especially those of $T_3$ and $T_8$ for the particles involved?