We compute the leading and sub-leading spin effects through the second
post-Newtonian order (2PN) in spherical harmonic modes of gravitational
waveforms from inspiralling compact binaries in non-circular orbits with
non-precessing components. The two spin couplings, linear-in-spin (spin-orbit;
SO) and quadratic-in-spin (spin-spin; SS), that appear in 2PN waveforms are
computed with desired accuracy and explicit expressions for relevant modes are
derived. The modes that have spin corrections through 2PN include (β,β£mβ£)=((2,2),(2,1),(3,3),(3,2),(3,1),(4,3),(4,1)) modes. Closed
form expressions for these modes for compact binaries in general orbits as well
as in elliptical orbits are being provided. While the general orbit results can
be used to study signals from binaries in orbits of arbitrary shape and nature,
elliptical orbit results are applicable to systems with arbitrary
eccentricities. We also express the elliptical orbit results as leading
eccentric corrections to the circular results. Our prescription represents, the
first, fully analytical treatment that combines spins, eccentricity and higher
modes together and completes computation of spin effects through 2PN order.
These should find immediate applications in inspiral-merger-ringdown modelling
for eccentric mergers including the effect of non-precessing spins and higher
modes as well as in parameter estimation analyses employing inspiral waveform