  Methylamine has been the only simple alkylamine detected in the interstellar
medium for a long time. With the recent secure and tentative detections of
vinylamine and ethylamine, respectively, dimethylamine has become a promising
target for searches in space. Its rotational spectrum, however, has been known
only up to 45 GHz until now. Here we investigate the rotation-tunneling
spectrum of dimethylamine in selected regions between 76 and 1091 GHz using
three different spectrometers in order to facilitate its detection in space.
The quantum number range is extended to $J = 61$ and $K_a = 21$, yielding an
extensive set of accurate spectroscopic parameters. To search for
dimethylamine, we refer to the spectral line survey ReMoCA carried out with the
Atacama Large Millimeter/submillimeter Array toward the high-mass star-forming
region Sagittarius B2(N) and a spectral line survey of the molecular cloud
G+0.693$-$0.027 employing the IRAM 30 m and Yebes 40 m radio telescopes. We
report nondetections of dimethylamine toward the hot molecular cores Sgr
B2(N1S) and Sgr B2(N2b) as well as G+0.693$-$0.027 which imply that
dimethylamine is at least 14, 4.5 and 39 times less abundant than methylamine
toward these sources, respectively. The observational results are compared to
computational results from a gas-grain astrochemical model. The modeled
methylamine to dimethylamine ratios are compatible with the observational lower
limits. However, the model produces too much ethylamine compared with
methylamine which could mean that the already fairly low levels of
dimethylamine in the models may also be too high.
