In the absence of any hints of new physics in LHC, TeV dark matter candidates interacting through electroweak force (EWDM) are still highly motivated. We extend the Standard Model by adding an arbitrary SU(2) DM multiplet in non-chiral representation. In addition to the well-known real representation which has no coupling to the nuclei at tree level, the complex representation can lead to a new DM candidate providing that one includes a higher dimensional mass-splitting operator, which survives the current direct detection bounds. Since the masses of gauge mediators are light compared to the dark particles, Sommerfeld effect is dominant and affects the value of annihilation cross-section in both the early universe and current time. We computed the relic abundance through freeze-out mechanism in order to determine DM mass. Gamma ray fluxes in our galaxy and dwarf satellites provide a promising tool to probe EWDM theory. We confronted the four fermionic representations of the model with the latest astrophysical observations. It can be concluded that the model passes the current experimental constraints successfully, and it is accessible to future observations.
