Left panels: GLS periodograms of the CARMENES and HIRES Doppler measurements combined and separately after consecutive subtraction of the GJ 1148 b and c planetary signals. Right panels: GLS peridograms of the CARMENES and HIRES activity indicators of GJ 1148. Horizontal lines show the FAP levels of 10% (dotted line), 1% (dot-dashed line), and 0.1% (dashed line). The S- and H-index measurements from the HIRES data and the CARMENES activity indicators have no power at the period of the planets GJ 1148 b and c (vertical blue dashed lines). The photometric measurements from SuperWASP, NSVS, and HATNet are densely sampled, and thus most of the GLS power appears significant, but it cannot be associated with the RV signals. The most likely stellar rotation frequency is shown with a red dashed line, while the red shaded area denotes its uncertainties, as given by Díez Alonso et al. (2019).