Brain structure and many brain functions are known to be genetically controlled, but direct links between neuroimaging measures and their underlying cellular‐level determinants remain largely undiscovered. Here, we adopt a novel computational method for examining potential similarities in high‐dimensional brain imaging data between siblings. We examine oscillatory brain activity measured with magnetoencephalography (MEG) in 201 healthy siblings and apply Bayesian reduced‐rank regression to extract a low‐dimensional representation of familial features in the participants' spectral power structure. Our results show that the structure of the overall spectral power at 1–90 Hz is a highly conspicuous feature that not only relates siblings to each other but also has very high consistency within participants' own data, irrespective of the exact experimental state of the participant. The analysis is extended by seeking genetic associations for low‐dimensional descriptions of the oscillatory brain activity. The observed variability in the MEG spectral power structure was associated with SDK1 (sidekick cell adhesion molecule 1) and suggestively with several other genes that function, for example, in brain development. The current results highlight the potential of sophisticated computational methods in combining molecular and neuroimaging levels for exploring brain functions, even for high‐dimensional data limited to a few hundred participants.