In this work, we study the possibility that dark matter fields transform in the ð1; 0Þ ⊕ ð0; 1Þ representation of the homogeneous Lorentz group. In an effective theory approach, we study the lowest-dimension interacting terms of dark matter with standard model fields, assuming that dark matter fields transform as singlets under the standard model gauge group. There are three dimension-four operators, two of them yielding a Higgs portal to dark matter. The third operator couples the photon and Z 0 fields to the higher multipoles of dark matter, yielding a spin portal to dark matter. For low mass dark matter (D), the decays Z 0 →DD and H →DD are kinematically allowed and contribute to the invisible widths of the Z 0 and H bosons. We use experimental results on these invisible widths to constrain the values of the low-energy constants g t (for the spin portal) and g s , g p (for the Higgs portal) for this mass region. We calculate the dark matter relic density in our formalism and, using the above constraints, we find that consistency with the experimental value requires dark matter to have a mass M > 43 GeV in the case of the spin portal and M > 62 GeV for the Higgs portal. For higher mass dark matter (M > M H =2), we calculate the velocity averaged cross section for the annihilation of dark matter intobb and τ þ τ − and compare with the upper bounds recently reported by Fermi-LAT and DES Collaborations, finding that both portals yield results consistent with the reported upper bounds. Finally, we study direct detection by elastic scattering on nuclei. The Higgs portal yields results consistent with the upper bounds reported recently by the XENON Collaboration. The spin portal can also accommodate this data but requires higher values of the dark matter mass or smaller values of the corresponding coupling.