A recent quantitative measurement of rates of new particle formation (NPF) in urban Shanghai showed that the high rates of NPF can be largely attributed to the sulfuric acid (SA)-dimethylamine (DMA) nucleation due to relatively high DMA concentration in urban atmosphere (Yao et al., Science. 2018, 361, 278). In certain atmospheric conditions, the release of DMA is accompanied with the emission of high concentration of ammonia. As a result, the ammonia (A) may participate in SA-DMA-based NPF. However, the main sources of DMA and A can be different, thereby leading to different mechanism for the SA-DMA-A-based nucleation under different atmospheric conditions. Near industrial sources with relatively high DMA concentration of 10 molecules cm, the contribution of binary SA-DMA nucleation to cluster formation is 61% at 278 K, representing a dominant pathway for NPF. However, in the region not too close to major source of DMA emission, e.g., near agriculture farmland, the routes involving ternary SA-DMA-A nucleation make a 64% contribution at 278 K with DMA concentration of 10 molecules cm, showing that A has marked impact on the cluster formation. Under such a condition, we predict that coexisting DMA and A could be detected in the process of NPF. Moreover, at winter temperatures or at higher altitudes, our calculations suggest that the clustering of initial clusters likely involve ternary SA-DMA-A clusters rather than binary SA-DMA clusters. These new insights may be helpful to analyze and predict atmospheric-condition-dependent NFP in either urban or rural regions and/or in different season of the year.