We report an analysis of the dust disk around DM~Tau, newly observed with the Atacama Large Millimeter/submillimeter Array (ALMA) at 1.3 mm. The ALMA observations with high sensitivity (8.4~$mu$Jy/beam) and high angular resolution (35~mas, 5.1~au) detect two asymmetries on the ring at $rsim$20~au. They could be two vortices in early evolution, the destruction of a large scale vortex, or double continuum emission peaks with different dust sizes. We also found millimeter emissions with $sim$50~$mu$Jy (a lower limit dust mass of 0.3~$M_{rm Moon}$) inside the 3-au ring. To characterize these emissions, we modeled the spectral energy distribution (SED) of DM~Tau using a Monte Carlo radiative transfer code. We found that an additional ring at $r=$ 1~au could explain both the DM~Tau SED and the central point source. The disk midplane temperature at the 1-au ring calculated in our modeling is less than the typical water sublimation temperature of 150~K, prompting the possibility of forming small icy planets there.