We present the detection of three super-Earths transiting the cool star LP415-17 , monitored by K2 mission in its 13 ^ { th } campaign .
High resolution spectra obtained with HARPS-N/TNG showed that the star is a mid-late K dwarf .
Using spectral synthesis models we infer its effective temperature , surface gravity and metallicity and subsequently determined from evolutionary models a stellar radius of 0.58 R _ { \odot } .
The planets have radii of 1.8 , 2.6 and 1.9 R _ { \oplus } and orbital periods of 6.34 , 13.85 and 40.72 days .
High resolution images discard any significant contamination by an intervening star in the line of sight .
The orbit of the furthest planet has radius of 0.18 AU , close to the inner edge of the habitable zone .
The system is suitable to improve our understanding of formation and dynamical evolution of super-Earth systems in the rocky – gaseous threshold , their atmospheres , internal structure , composition and interactions with host stars .