  We present the detection of three super-Earths transiting the cool star
LP415-17, monitored by K2 mission in its 13th 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 subse- quently determined from evolutionary models a
stellar radius of 0.58 R Sun. The planets have radii of 1.8, 2.6 and 1.9 R
Earth 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.
