  Additional low-amplitude signals are observed in many RR Lyrae stars, beside
the pulsations in radial modes. The most common ones are short-period signals
forming a period ratio of around 0.60--0.65 with the first overtone, or
long-period signals forming a period ratio of around 0.68. The RR Lyrae stars
may also exhibit quasi-periodic modulation of the light curves, known as the
Blazhko effect. We used the extensive sample of the first-overtone RR Lyrae
stars observed by the Kepler telescope during the K2 mission to search for and
characterize these low-amplitude additional signals. K2 data provides
space-based photometry for a statistically significant sample. Hence this data
is excellent to study in detail pulsation properties of RR Lyrae stars. We used
K2 space-based photometry for RR Lyrae candidates from Campaigns 0-19. We
selected RR Lyrae stars pulsating in the first overtone and performed a
frequency analysis for each star to characterize their frequency contents. We
classified 452 stars as first-overtone RR Lyrae. From that sample, we selected
281 RR$_{0.61}$ stars, 67 RR$_{0.68}$ stars, and 68 Blazhko stars. We found
particularly interesting stars which show all of the above phenomena
simultaneously. We detected signals in RR$_{0.61}$ stars that form period
ratios lower than observed for the majority of stars. These signals likely form
a new sequence in the Petersen diagram, around a period ratio of 0.60. In 32
stars we detected additional signals that form a period ratio close to that
expected in RRd stars, but the classification of these stars as RRd is
uncertain. We also report a discovery of additional signals in eight stars that
form a new group in the Petersen diagram around the period ratio of
0.465-0.490. The nature of this periodicity remains unknown.
