Technically, only one of them generates a first class constraint, while the
others generate a second-class
constraint. There are, therefore,
additional secondary constraints to be found by commuting the
primary constraint with the Hamiltonian, but the presence of these constraints at the linear level ensures that
they must exist at the non-linear level. There is also another subtlety in obtaining the secondary constraints
associated with the fact that the Hamiltonian is pure constraint, see the discussion in Section 7.1.3 for more
details.