} \begin{split} & E_{u_{0},u_{0}}(\tau+b)=  e^{\pi i b B_{0}(u_{0})} E_{u_{0},u_{0}+b u_{0}}(\tau) , \ \ \ \ \mathrm{for } \ c = 0 , \\ \\  & E_{u_{0},u_{0}}(\gamma (\tau))= \varepsilon (a,b,c,d) e^{\pi i \delta} E_{u_{0}^{\prime},u_{0}^{\prime}}(\tau) , \ \ \ \ \mathrm{for } \ c\neq 0, \end{split}$$  where  $$\