Context : SN2011fe was detected by the Palomar Transient Factory on August 24th 2011 in M101 a few hours after the explosion .
From the early optical spectra it was immediately realized that it was a Type Ia supernova thus making this event the brightest one discovered in the last twenty years .

Aims : The distance of the event offered the rare opportunity to perform a detailed observation with the instruments on board of INTEGRAL to detect the \gamma –ray emission expected from the decay chains of ^ { 56 } Ni .
The observations were performed in two runs , one before and around the optical maximum , aimed to detect the early emission from the decay of ^ { 56 } Ni and another after this maximum aimed to detect the emission of ^ { 56 } Co .

Methods : The observations performed with the instruments on board of INTEGRAL ( SPI , IBIS/ISGRI , JEMX and OMC ) have been analyzed and compared with the existing models of \gamma –ray emission from such kind of supernovae .
In this paper , the analysis of the \gamma –ray emission has been restricted to the first epoch .

Results : Both , SPI and IBIS/ISGRI , only provide upper-limits to the expected emission due to the decay of ^ { 56 } Ni .
These upper-limits on the gamma-ray flux are of 7.1 \times 10 ^ { -5 } ph/s/cm ^ { 2 } for the 158 keV line and of 2.3 \times 10 ^ { -4 } ph/s/cm ^ { 2 } for the 812 keV line .
These bounds allow to reject at the 2 \sigma level explosions involving a massive white dwarf , \sim 1 M \odot in the sub–Chandrasekhar scenario and specifically all models that would have substantial amounts of radioactive ^ { 56 } Ni in the outer layers of the exploding star responsible of the SN2011fe event .
The optical light curve obtained with the OMC camera also suggests that SN2011fe was the outcome of the explosion , possibly a delayed detonation although other models are possible , of a CO white dwarf that synthesized \sim 0.55 M _ { \odot } of ^ { 56 } Ni .
For this specific model , INTEGRAL would have only been able to detect this early \gamma –ray emission if the supernova had occurred at a distance \la 2 Mpc .

Conclusions : The detection of the early \gamma –ray emission of ^ { 56 } Ni is difficult and it can only be achieved with INTEGRAL if the distance of the event is close enough .
The exact distance depends on the specific SNIa subtype .
The broadness and rapid rise of the lines are probably at the origin of such difficulty .