  De Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations of the
organic metal $\theta$-(BETS) 4 CoBr 4 (C 6 H 4 Cl 2) are studied in magnetic
fields of up to 55 T at liquid helium temperatures. In line with Fermi surfaces
(FS) illustrating the linear chain of coupled orbits, the observed Fourier
components are linear combinations of the frequencies linked to the two basic
orbits $\alpha$ and $\beta$, which have small effective masses compared to
other organic metals with the same FS topology. Analytical formulas based on a
second order development of the free energy within the canonical ensemble, not
only account for the field and temperature dependence of the dHvA amplitudes
but also for their relative values. In addition, strongly non-Lifshitz-Kosevich
behaviours are quantitatively interpreted. In contrast, Shubnikov-de Haas
oscillations are not accounted for by this model. short title: Quantum
oscillations of $\theta$-(BETS) 4 CoBr 4 (C 6 H 4 Cl 2)
