  Recently, Brannan and Vergnioux showed that the free orthogonal quantum group
factors $\mathcal{L}\mathbb{F}O_M$ have Jung's strong 1-boundedness property,
and hence are not isomorphic to free group factors. We prove an analogous
result for the other unimodular case, where the parameter matrix is the
standard symplectic matrix in 2N dimensions $J_{2N}$. We compute free
derivatives of the defining relations by introducing self-adjoint generators
through a decomposition of the fundamental representation in terms of Pauli
matrices, resulting in 1-boundedness of these generators. Moreover, we prove
that under certain conditions, one can add elements to a 1-bounded set without
losing 1-boundedness. In particular this allows us to include the character of
the fundamental representation, proving strong 1-boundedness.
