  We derive the kinematic Hamiltonian for the so-called "new general
relativity" class of teleparallel gravity theories, which is the most general
class of theories whose Lagrangian is quadratic in the torsion tensor and does
not contain parity violating terms. Our approach makes use of an explicit
expression for the flat, in general, nonvanishing spin connection, which avoids
the use of Lagrange multipliers, while keeping the theory invariant under local
Lorentz transformations. We clarify the relation between the dynamics of the
spin connection degrees of freedom and the tetrads. The terms constituting the
Hamiltonian of the theory can be decomposed into irreducible parts under the
rotation group. Using this, we demonstrate that there are nine different
classes of theories, which are distinguished by the occurrence or
non-occurrence of certain primary constraints. We visualize these different
classes and show that the decomposition into irreducible parts allows us to
write the Hamiltonian in a common form for all nine classes, which reproduces
the specific Hamiltonians of more restricted classes in which particular
primary constraints appear.
