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We obtain the complete and independent bases of effective operators at massdimension 5, 6, 7, 8, 9 in both standard model effective field theory withlight sterile right-handed neutrinos ($\nu$SMEFT) and low energy effectivefield theory with light sterile neutrinos ($\nu$LEFT). These theories providesystematical parametrizations on all possible Lorentz-invariant physicaleffects involving in the Majorana/Dirac neutrinos, with/without the leptonnumber violations. In the $\nu$SMEFT, we find that there are 2 (18), 29 (1614),80 (4206), 323 (20400), 1358 (243944) independent operators with sterileneutrinos included at the dimension 5, 6, 7, 8, 9 for one (three) generation offermions, while 24, 5223, 3966, 25425, 789426 independent operators in the$\nu$LEFT.

Operator Bases in Effective Field Theories with Sterile Neutrinos: $d \leq 9$