We present a new analysis of stellar mass functions in the COSMOS field to fainter limits than has been previously probed at z \leq 1 . The increase in dynamic range reveals features in the shape of the stellar mass function that deviate from a single Schechter function . Neither the total nor the red ( passive ) or blue ( star-forming ) galaxy stellar mass functions can be well fit with a single Schechter function once the mass completeness limit of the sample probes below \sim 3 \times 10 ^ { 9 } \mathrm { M _ { \odot } } . We observe a dip or plateau at masses \sim 10 ^ { 10 } \mathrm { M _ { \odot } } , just below the traditional M ^ { * } , and an upturn towards a steep faint-end slope of \alpha \sim - 1.7 at lower mass at all redshifts \leq 1 . This bimodal nature of the mass function is not solely a result of the blue/red dichotomy . Indeed , the blue mass function is by itself bimodal at z \sim 1 . This suggests a new dichotomy in galaxy formation that predates the appearance of the red sequence . We propose two interpretations for this bimodal distribution . If the gas fraction increases towards lower mass , galaxies with M _ { baryon } \sim 10 ^ { 10 } \mathrm { M _ { \odot } } would shift to lower stellar masses , creating the observed dip . This would indicate a change in star formation efficiency , perhaps linked to supernovae feedback becoming much more efficient below \sim 10 ^ { 10 } \mathrm { M _ { \odot } } . Therefore , we investigate whether the dip is present in the baryonic ( stars+gas ) mass function . Alternatively , the dip could be created by an enhancement of the galaxy assembly rate at \sim 10 ^ { 11 } \mathrm { M _ { \odot } } , a phenomenon that naturally arises if the baryon fraction peaks at M _ { halo } \sim 10 ^ { 12 } \mathrm { M _ { \odot } } . In this scenario , galaxies occupying the bump around M _ { \ast } would be identified with central galaxies and the second fainter component of the mass function having a steep faint-end slope with satellite galaxies . The low-mass end of the blue and total mass functions exhibit a steeper slope than has been detected in previous work that may increasingly approach the halo mass function value of -2 . While the dip feature is apparent in the total mass function at all redshifts , it appears to shift from the blue to red population , likely as a result of transforming high-mass blue galaxies into red ones . At the same time , we detect a drastic upturn in the number of low-mass red galaxies . Their increase with time seems to reflect a decrease in the number of blue systems and so we tentatively associate them with satellite dwarf ( spheroidal ) galaxies that have undergone quenching due to environmental processes .