With the goal of searching for very low modulation amplitudes among fundamental mode RR Lyrae stars and assess their incidence rate, we performed a survey of 36 stars observed by the Kepler satellite during the entire four-year period of its mission. The search was conducted by a task-oriented code, designed to find low-amplitude signals in the presence of high-amplitude components and instrumental systematics. We found 7 new modulated stars and negate one earlier claimed star, whereby increasing the number of known Blazhko stars from 17 to 24 and yielding an observed occurrence rate of 67% for the Kepler field. Six of the new stars have the lowest modulation amplitudes found so far, with ~250 ppm Fourier side-lobe amplitudes near the fundamental mode frequency. Because of the small sample size in the Kepler field, we extended the survey to 12 campaign fields observed by K2, the ``two-wheeled'' mission of Kepler. From the 1061 stars we found 514 Blazhko stars. After correcting for the short duration of the time spent on each field, and for the noise dependence of the detections, we arrived at an underlying occurrence rate of ~75% - likely a lower limit for the true rate of Blazhko stars in the K2 fields.
Comment: Submitted to Astronomy and Astrophysics; after the first (positive) referee report; 11 pages with 10 figures; lightweight, with 1.7 Mb; nice, old-format references linked to paper abstracts