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