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We compute the leading and sub-leading spin effects through the secondpost-Newtonian order (2PN) in spherical harmonic modes of gravitationalwaveforms from inspiralling compact binaries in non-circular orbits withnon-precessing components. The two spin couplings, linear-in-spin (spin-orbit;SO) and quadratic-in-spin (spin-spin; SS), that appear in 2PN waveforms arecomputed with desired accuracy and explicit expressions for relevant modes arederived. The modes that have spin corrections through 2PN include $(\ell,|m|)$=$((2,2),\,(2,1),\,(3,3),\,(3,2),\,(3,1),\,(4,3),\,(4,1))$ modes. Closedform expressions for these modes for compact binaries in general orbits as wellas in elliptical orbits are being provided. While the general orbit results canbe used to study signals from binaries in orbits of arbitrary shape and nature,elliptical orbit results are applicable to systems with arbitraryeccentricities. We also express the elliptical orbit results as leadingeccentric corrections to the circular results. Our prescription represents, thefirst, fully analytical treatment that combines spins, eccentricity and highermodes together and completes computation of spin effects through 2PN order.These should find immediate applications in inspiral-merger-ringdown modellingfor eccentric mergers including the effect of non-precessing spins and highermodes as well as in parameter estimation analyses employing inspiral waveform.

Spin effects in Spherical Harmonic Modes of Gravitational Waves from Eccentric Compact Binary Inspirals