The work based on spectral observations from Sayan Solar Observatory (SSO) is aimed at searching for signs that indicate a connection between oscillatory motions in the filament and the lower layers of the solar atmosphere. We also figure out on which scales transverse oscillations are detected in the filament. We analyze the simultaneously obtained time series of intensities and variations in the Doppler velocity in the photosphere (FeI λ 4897 Å) and in the chromosphere (Hβ λ 4861 Å) in the region of a large quiescent filament at its different positions on the Sun. In the distribution of the small-amplitude Doppler velocity oscillations beyond the filament and on its edge, we have found small areas, where wavelet spectra within 2–4 mHz in the chromosphere coinciding with the wavelet spectra in the photosphere. In the filament transverse (horizontal) displacements in the sky plane, we have revealed oscillations of two types. Individual filament structures (about 2"–4" in size) oscillate transversely within 5>f>1 mHz at the 0.3–2.1 Mm displacement amplitude. The transverse oscillation spectrum of the filament fragment at its position on the central meridian demonstrates two frequency ranges: 5>f>1 mHz and ~0.5 mHz. There is only one peak (~0.26 mHz) in the spectrum when the filament moves away from the Sun’s central meridian.