  Let $M$ be a finitely generated module over a Noetherian local ring. This
paper gives, for a given parameter ideal $Q$ for $M$, bounds for the second
Hilbert coefficients ${\mathrm{e}}_Q^2(M)$ in terms of the homological degrees
and torsions of modules. We also report a criterion for a certain equality of
the second Hilbert coefficients of parameters and the homological torsions of
modules.
