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Interaction of three-dimensional magnetic fields, turbulence, andself-gravity in the molecular cloud is crucial in understanding star formationbut has not been addressed so far. In this work, we target the low-massstar-forming region L1688 and use the spectral emissions of $^{12}$CO,$^{13}$CO, C$^{18}$O, and H I, as well as polarized dust emissions. To obtainthe 3D direction of the magnetic field, we employ the novel polarizationfraction analysis. In combining with the plane-of-the-sky (POS) magnetic fieldstrength derived from the Davis-Chandrasekhar-Fermi (DCF) method and the newDifferential Measure Analysis (DMA) technique, we present the first measurementof L1688's three-dimensional magnetic field, including its orientation andstrength. We find that L1688's magnetic field has two statistically differentinclination angles. The low-intensity tail has an inclination angle$\approx55^\circ$ on average, while that of the central dense clump is$\approx30^\circ$. We find the global mean value of total magnetic fieldstrength is $B_{\rm tot}\approx135$ uG from DCF and $B_{\rm tot}\approx75$ uGfrom DMA. We use the velocity gradient technique (VGT) to separate the magneticfields' POS orientation associated with L1688 and its foreground/background.The magnetic fields' orientations are statistically coherent. The probabilitydensity function of H$_2$ column density and VGT reveal that L1688 ispotentially undergoing gravitational contraction at large scale $\approx1.0$ pcand gravitational collapse at small scale $\approx0.2$ pc. The gravitationalcontraction mainly along the magnetic field results in an approximate power-lawrelation $B_{\rm tot}\propto n_{\rm H}^{1/2}$ when volume density $n_{\rm H}$is less than approximately $6.0\times10^3$ cm$^{-3}$.

Characterizing three-dimensional magnetic field, turbulence, and self-gravity in the star-forming region L1688