The fourth moment of Dirichlet L-functions along the critical line

For a positive integer $q\equiv ̸2(\mathrm{m}\mathrm{o}\mathrm{d}4)$, this work considers the fourth moment of Dirichlet $L$-functions averaged over both $t\in [0,T]$ and primitive characters to modulus $q$. An asymptotic formula with a power saving from both $q$-aspect and $t$-aspect in the error term is obtained.