Fractionally filled Chern bands with strong interactions may give rise to fractional Chern insulator(FCI) states, the zero-field analogue of the fractional quantum Hall effect. Recent experiments have demonstrated the existence of fractional Chern insulators (FCIs) in twisted bilayer MoTe2 without external magnetic fields most robust at ν = −2/3 as well as Chern insulators (CIs) at ν = −1. Although the appearance of both of these states is theoretically natural in an interacting topological system, experiments repeatedly observe nonmagnetic states (lacking FCIs) at ν = −1/3 and −4/3, a puzzling result which has not been fully theoretically explained. In this talk, we will discuss how the standard MoTe2 moiré model can capture the non-magnetic states at ν = −1/3 and −4/3 in unison with the FCI at ν = −2/3 and CI state at ν = −1. In particular, we will show the importance of remote bands in identifying the competing magnetic orders.