The MAGIC collaboration has recently reported the discovery of \gamma -ray emission from the binary system LS I +61 ^ { \circ } 303 in the TeV energy region .
Here we present new observational results on this source in the energy range between 300 \textrm { GeV } and 3 \textrm { TeV } .
In total 112 hours of data were taken between September and December 2006 covering 4 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 ^ { \circ } 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 \Gamma = 2.6 \pm 0.2 _ { stat } \pm 0.2 _ { sys } .
LS I +61 ^ { \circ } 303 was found to be variable at TeV energies on timescales of days .
These new MAGIC measurements allowed us to search for intra-night variability of the VHE emission ; however , no evidence for flux variability on timescales down to 30 minutes 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 ^ { \circ } 303 data taken in 2005 and 2006 .
We found the LS I +61 ^ { \circ } 303 data set to be periodic with a period of ( 26.8 \pm 0.2 ) days ( with a post-trial chance probability of 10 ^ { -7 } ) , close to the orbital period .