Context. The carbon-rich envelope of the asymptotic giant branch star CW Leo, IRC+10216, is one of the richest molecular sources in the sky. Available spectral surveys below 51 GHz are more than 25 years old, and new work is needed. Aims. Characterizing the rich molecular content of this source, specially for heavy species, requires carrying out very sensitive spectral surveys at low frequencies. In particular, we have achieved an rms in the range 0.2-0.6 mK per MHz. Methods. Long Q band

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... 0.3 GHz) single-dish integrations were carried out with the Yebes-40m telescope using specifically built receivers. The most recent line catalogs were used to identify the lines. Results. The data contain 652 spectral features, corresponding to 713 transitions from 81 species (we count the isomers, isotopologs, and ortho/para species separately). Only 57 unidentified lines remain with signal-to-noise ratios 3. Some new species and/or vibrational modes have been discovered for the first time with this survey. Conclusions. This IRC+10216 spectral survey is by far the most sensitive survey carried out to date in the Q band. It therefore provides the most complete view of IRC+10216 from 31.0 to 50.3 GHz, giving unique information about its molecular content, especially for heavy species. Rotational diagrams built from the data provide valuable information about the physical conditions and chemical content of this circumstellar envelope.