A sample of the LAMOST spectra of the early type M0-M3 dwarfs is compared with the Kepler observations. It is found that M dwarfs with strong chromospheric emission in $H_{alpha}$ have large flare activity in general. The rotational periods derived from the Kepler measurements have close correlations with the sizes of the flares, the power-law distribution index and the equivalent widths of the $H_{alpha}$ emission. A clear trend exists for higher magnetic activities being detected in faster rotating M dwarfs (rotation periods $<$ 20 day).