We measured the trigonometric parallax of the H_2_O maser source associated with the L1482 molecular filament hosting the most massive young star, LkH{alpha} 101, in the California molecular cloud. The measured parallax is 1.879+/-0.096mas, corresponding to the distance of 532+/-28pc. This parallax is consistent with that of the nearby star cluster LkH{alpha} 101, which was recently measured with Gaia DR2. We found that the L1482 molecular filament and the LkH{alpha} 101 cluster are located at the same distance within 3+/-30pc. We observed the southern parts of L1482 molecular clouds including the H_2_O maser source, which is adjacent to LkH{alpha} 101, using the Nobeyama 45m telescope in the J=1-0 transitions of both ^12^CO and ^13^CO. The peak intensity of the ^12^CO line revealed the high excitation temperature region (60-70K) due to heating by UV radiation from LkH{alpha} 101. We derived the column density of these molecular clouds assuming local thermodynamic equilibrium (LTE) from the ^13^CO emission. Using Dendrogam, we searched for small-scale, dense structures (cores) and identified 337 cores in the ^13^CO data. Gravitationally bound cores with a virial mass to LTE mass ratio <=1.5 and young stars are concentrated in the high excitation temperature region. The column density in the warm region is five to six times larger than that of the surrounding colder molecular region. This suggests that the warm region has been compressed by a high-pressure wave and successive radiation-driven star formation is in progress in this warm region. In the cold molecular cloud to the north of the warm region, the cores are likely gravitationally unbound, which may be the reason why star formation is not active there.