  The resource theoretic measure of quantum coherence is basis dependent, and
the amount of coherence contained in a state is different in different bases.
We obtained analytical solutions for the maximum coherence by optimizing the
reference basis and highlighted the essential role of the mutually unbiased
bases (MUBs) on attaining the maximum coherence. Apart from the relative
entropy of coherence, we showed that the MUBs are optimal for the robustness of
coherence, the coherence weight, and the modified skew information measure of
coherence for any state. Moreover, the MUBs are optimal for all the faithful
coherence measures if the state is pure or is of the single qubit. We also
highlighted an upper bound for the $l_1$ norm of coherence and compared it with
the other bounds as well as the maximum one attainable by optimizing the
reference basis.
