An important feature of turbulent boundary layers are persistent large-scale coherent structures in the flow. Here, we use Dynamic Mode Decomposition (DMD), a data-driven technique designed to detect spatio-temporal coherence, to construct optimal low-dimensional representations of such large-scale dynamics in the asymptotic suction boundary layer (ASBL). In the ASBL, fluid is removed by suction through the bottom wall, resulting in a constant boundary layer thickness in streamwise direction. That is, the streamwise advection of coherent structures by the mean flow ceases to be of dynamical importance and can be interpreted as a continuous shift symmetry in streamwise direction. However, this results in technical difficulties, as DMD is known to perform poorly in presence of continuous symmetries. We address this issue using symmetry-reduced DMD (Marensi et al., 2023), and find the large-scale dynamics of the ASBL to be low-dimensional indeed and potentially self-sustained, featuring ejection and sweeping events at large scale. Interactions with near-wall structures are captured when including only a few more modes.(c) 2023 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).