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The analysis of a physical problem simplifies considerably when one uses asuitable coordinate system. We apply this approach to the discrete-time quantumwalks with coins given by $2j+1$-dimensional Wigner rotation matrices (Wignerwalks), a model which was introduced in T. Miyazaki et al., Phys. Rev. A 76,012332 (2007). First, we show that from the three parameters of the coinoperator only one is physically relevant for the limit density of the Wignerwalk. Next, we construct a suitable basis of the coin space in which the limitdensity of the Wigner walk acquires a much simpler form. This allows us toidentify various dynamical regimes which are otherwise hidden in the standardbasis description. As an example, we show that it is possible to find aninitial state which reduces the number of peaks in the probability distributionfrom generic $2j+1$ to a single one. Moreover, the models with integer $j$ leadto the trapping effect. The derived formula for the trapping probabilityreveals that it can be highly asymmetric and it deviates from purelyexponential decay. Explicit results are given up to the dimension five.

Suitable bases for quantum walks with Wigner coins