Top panels: full spectrum observed with the IRAM 30 m telescope towards the cold dense core in TMC-1C. The mean rms noise level is ~2 mK. Most of the detected lines emit only in one channel (channel width 0.5–0.7 km s^-1), suggesting that the linewidth of the different lines is ≤0.7 km s^-1 (see Sect. 3.2). Bottom panels: close-up views of the frequency ranges around the brightest transitions of the CO-H₂ van der Waals complex. The corresponding frequencies are listed in Table 1, and are shown in the panels with a vertical dotted line. The expected linewidth is ≈0.3 km s^-1, as measured in higher spectral resolution observations (e.g. Spezzano et al. 2013).