In the present study, thermoacoustic oscillations of a flame propagating from an open to a closed endof an narrow channel with adiabatic walls are studied numerically. The study revisits the importance ofhydrodynamic instability and flame symmetry for both primary and secondary acoustic instabilities. For a nonsymmetric slanted flame, the primary instability is linked to the development of the hydrodynamic instability,resulting in a corrugated flame front. Spectral Proper Orthogonal Decomposition (SPOD) was employed todemonstrate that the mode at the fundamental frequency is closely associated with the nonlinear behavior ofthe hydrodynamic cells at the flame front. For the secondary instability of a non-symmetric flame, resonancebetween the acoustic waves at the fundamental mode and the hydrodynamic modes was observed, without aclear emergence of the parametric instability. For a symmetric flame, the parametric acoustic instability canbe more easily observed in a narrow channel. For a symmetric flame, SPOD of the fundamental frequencysuggests the formation of a mixture pocket at the centerline, that can potentially invert the flame front, whilethe first harmonic is related to the flame front inversion process.