  In this article, we characterize the $UMD$--property of a Banach space $X$ by
ideal norms associated with trigonometric orthonormal systems.
  The asymptotic behavior of that numerical parameters can be used to decide
whether or not $X$ is a $UMD$--space. Moreover, in the negative case, we obtain
a measure that shows how far $X$ is from being a $UMD$--space.
  The main result is, that all described parameters are equivalent also in the
quantitative setting.
