The evolution of blood flow is vital in understanding the pathogenesis of brain aneurysms. Several past studies have shown evidence for a turbulent inflow jet at the aneurysm neck. Although there is a great need for analyzing inflow jet dynamics in clinical practice, data summarized in noninvasive modalities such as Magnetic Resonance Imaging or Computed Tomography are usually limited by spatial and temporal resolutions, and thus cannot account for the hemodynamics. In this paper, Dynamic Mode Decomposition (DMD) is used to pinpoint the dominant modes of the inflow jet in patient-specific models of sidewall aneurysms. This paper aims to prove that the dynamic modes are inflow jet interaction with the distal wall in addition to the hemodynamics of the parent artery. Our work indicates that DMD is an essential tool for analyzing blood flow patterns of brain aneurysms and is a promising tool to be used in in vivo context.