The MAGIC collaboration has recently reported the discovery of γ-ray emission from the binary system LS I +61°303 in the TeV energy region. Here we present new observational results on this source in the energy range between 300 GeV and 3 TeV. In total, 112 hr of data were taken between 2006 September and December covering four orbital cycles of this object. This large amount of data allowed us to produce an integral flux light curve covering for the first time all orbital phases of LS I +61°303. In addition, we also obtained a differential energy spectrum for two orbital phase bins covering the phase range 0.5 < phi < 0.6 and 0.6 < phi < 0.7. The photon index in the two phase bins is consistent within the errors with an average index Γ = 2.6 ± 0.2stat ± 0.2sys. LS I +61°303 was found to be variable at TeV energies on timescales of days. These new MAGIC measurements allowed us to search for intranight variability of the very high energy emission; however, no evidence for flux variability on timescales down to 30 min was found. To test for possible periodic structures in the light curve, we apply the formalism developed by Lomb and Scargle to the LS I +61°303 data taken in 2005 and 2006. We found the LS I +61°303 data set to be periodic with a period of (26.8 ± 0.2) days (with a post-trial chance probability of 10-7), close to the orbital period.