Context. The CoRoT -Convection Rotation and planetary Transits -space mission is a great opportunity for monitoring stars with excellent time-sampling and unprecedented photometric precision for up to 150 days. As an important benefit, high-quality RR Lyrae light curves are obtained with a quasi-uninterrupted coverage over several pulsation and Blazhko cycles. Aims. The Blazhko effect in RR Lyrae stars is an unsolved problem of astrophysics. We used the high-precision space data to contribute more precise knowledge to explain the possible physical processes behind the phenomenon. Methods. We applied different period-finding techniques including Period04, MuFrAn, PDM and SigSpec. Amplitude and phase modulation were investigated by an analytical function method as well as with the traditional O-C diagrams. Results. The Blazhko modulation frequency is directly detected in the spectrum, as well as its first and second harmonics. It shows the non-linear nature of the Blazhko modulation. Besides the triplets, further higher-order modulation side peaks appear around the pulsation frequency as quintuplet, septuplet, nonuplet, undecaplet, tredecaplet, quindecaplet and sepdecaplet structures. Additional frequencies, not belonging to the classical multiplet structures, are detected, as well as their linear combinations with the fundamental radial mode. We interpret these additional terms as non-radial modes. During the five consecutive Blazhko cycles, there is a shift of the maximum phase around 0.011 pulsation phase which is likely the consequence of a long term modulation.