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Rapid progress in cooling and trapping of molecules has enabled first experiments on high resolution spectroscopy of trapped diatomic molecules, promising unprecedented precision. Extending this work to polyatomic molecules provides unique opportunities due to more complex geometries and additional internal degrees of freedom. Here, this is achieved by combining a homogeneous-field microstructured electric trap, rotational transitions with minimal Stark broadening at a 'magic' offset electric field, and optoelectrical Sisyphus cooling of molecules to the low millikelvin temperature regime. We thereby reduce Stark broadening on the $J=5\leftarrow4$ ($K=3$) transition of formaldehyde at $364\,$GHz to well below $1\,$kHz, observe Doppler-limited linewidths down to $3.8\,$kHz, and determine the 'magic'-field line position with an uncertainty below $100\,$Hz. Our approach opens a multitude of possibilities for investigating diverse polyatomic molecule species.

We present precision spectroscopy on electrically trapped formaldehyde (H$_2$CO), demonstrating key attributes which will enable molecular spectroscopy with unprecedented precision. Our method makes use of a microstructured electric trap with homogeneous fields in the trap center and rotational transitions with minimal Stark broadening at a 'magic' offset electric field. Using molecules cooled to the low millikelvin temperature regime via optoelectrical Sisyphus cooling, we reduce Stark broadening on the $J=5\leftarrow4$ ($K=3$) transition at 364 GHz to well below 1 kHz, observe Doppler-limited linewidths down to 3.8 kHz, and determine the line position with sub-kHz uncertainty. Our results and clear prospects for even narrower spectra pave the way towards in-trap precision spectroscopy on diverse molecule species.

We demonstrate direct cooling of gaseous formaldehyde (H2CO) to the microkelvin regime. Our approach, optoelectrical Sisyphus cooling, provides a simple dissipative cooling method applicable to electrically trapped dipolar molecules. By reducing the temperature by three orders of magnitude and increasing the phase-space density by a factor of ~$10^4$ we generate an ensemble of $3\cdot10^5$ molecules with a temperature of about 420\mu K, populating a single rotational state with more than 80% purity.