We will present the discovery of a sub-Neptunian mass planet orbiting a nearby (d = 6.25 pc) M4.0 V star that was detected by our CARMENES radial-velocity (RV) survey. We determine a planetary minimum mass of Mb sin i = 5.46 ± 0.75 MÅ and an orbital period of Pb = 36.116 ± 0.029 d, using 5 yr of CARMENES data, as well as archival RVs from HARPS and HIRES spanning more than 9 yr. The flux received by the planet equals half the instellation on Earth, which places it in the middle of the conservative habitable zone of its host star. The RV data show evidence for another planet candidate with M[c] sin i = 9.7 ± 1.9 MÅ and P[c] = 113.46 ± 0.20 d. However, we cannot rule out stellar activity because of its proximity to the rotation period of the star. The discovery adds the sub-Neptunian mass planet to the short list of super-Earth planets in the habitable zone of M dwarfs, but the other planet candidate probably cannot be inhabited because, if confirmed, it would likely be an icy giant. These results are based on González-Álvarez et al. 2023, A&A in press, arXiv:2305.19677