\begin{table}%t6 \par \caption {\label{tab:photJ1751}Upper limits ($3\sigma$) on the optical counterpart of XTE~J1751$-$305.} %\centerline {\begin{tabular}{ccccc} \hline\hline Filter &${\lambda}_{\rm c}$& Limiting magnitude & $A_{\lambda}$ & Absolute mag \\ & (\AA) & & (mag) & \\ \hline $R$ & 6500 & $> $$23.1$ & $4.03 \pm 0.02$ & $>$$ 4.6$ \\ $I$ & 8000 & $> $$21.6$ & $2.91 \pm 0.02$ & $>$$ 4.2$ \\ $Z$ & 9625 & $> $$20.6$ & $2.12 \pm 0.02$ & $> $$4.0$ \\ $J$ & 12500 & $> $$19.6$ & $1.35 \pm 0.02$ & $> $$3.7$ \\ \hline \end{tabular}} Values in column three are uncorrected for reddening (from Jonker et~al. 2003). In column four are reported the dereddening parameters we used to correct for interstellar absorption computed assuming $E(B-V)=1.69 \pm 0.02$~mag The absolute magnitudes are computed assuming a distance of 8~kpc (Wijnands et~al. 2005; see Sect.~4.3.1 for details). \vspace*{-3mm} \end{table}