  The overtone and multi-mode RR Lyrae stars in the globular cluster M3 are
studied using a 200-d long, $B,V$ and $I_{\mathrm C}$ time-series photometry
obtained in 2012. 70\% of the 52 overtone variables observed show some kind of
multi-periodicity (additional frequency at ${f_{0.61}}={f_{\mathrm {1O}}}/0.61$
frequency ratio, Blazhko effect, double/multi-mode pulsation, period doubling).
A signal at 0.587 frequency ratio to the fundamental-mode frequency is detected
in the double-mode star, V13, which may be identified as the second radial
overtone mode. If this mode-identification is correct, than V13 is the first RR
Lyrae star showing triple-mode pulsation of the first three radial modes.
Either the Blazhko effect or the ${f_{0.61}}$ frequency (or both of these
phenomena) appear in 7 double-mode stars. The $P_{\mathrm{1O}}/P_{\mathrm{F}}$
period ratio of RRd stars showing the Blazhko effect are anomalous. A
displacement of the main frequency component at the fundamental-mode with the
value of modulation frequency (or its half) is detected in three Blazhko RRd
stars parallel with the appearance of the overtone-mode pulsation. The
${f_{0.61}}$ frequency appears in RRc stars that lie at the blue side of the
double-mode region and in RRd stars, raising the suspicion that its occurrence
may be connected to double-mode pulsation. The changes of the Blazhko and
double-mode properties of the stars are also reviewed using the recent and
archive photometric data.
