Monolayer NbSe$_2$ has recently been shown to be a 2-dimensional superconductor, with a competing charge-density wave (CDW) order. This work investigates the electronic structure of monolayer NbSe$_2$ based on first principles calculations, focusing on charge and magnetic orders in connection to the superconductivity. It is found that decreased screening in the monolayer NbSe$_2$ with a perfect lattice exhibits magnetic instability, which is removed by the formation of CDW. Two energetically competitive but distinct $3times3$ CDW structures are revealed computationally, which have a significant impact on the Fermi surface. The relations of the potential CDW phases with experimental structure and the coexisting superconductivity are discussed.
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