The very high energy (VHE; >100 GeV) source HESS J0632+057 has been recently confirmed as a gamma-ray binary, a subclass of the high mass X-ray binary (HMXB) population, through the detection of an orbital period of 321 days. We performed a deep search for the emission of HESS J0632+057 in the GeV energy range using data from the Fermi Large Area Telescope (LAT). The analysis was challenging due to the source being located in close proximity to the bright gamma-ray pulsar PSR J0633+0632 and lying in a crowded region of the Galactic plane where there is prominent diffuse emission. We formulated a Bayesian block algorithm adapted to work with weighted photon counts, in order to define the off-pulse phases of PSR J0633+0632. A detailed spectral-spatial model of a 5 deg circular region centred on the known location of HESS J0632+057 was generated to accurately model the LAT data. No significant emission from the location of HESS J0632+057 was detected in the 0.1-100 GeV energy range integrating over ~3.5 years of data; with a 95% flux upper limit of F_{0.1-100 GeV} < 3 x 10-8 ph cm-2 s-1. A search for emission over different phases of the orbit also yielded no significant detection. A search for source emission on shorter timescales (days--months) did not yield any significant detections. We also report the results of a search for radio pulsations using the 100-m Green Bank Telescope (GBT). No periodic signals or individual dispersed bursts of a likely astronomical origin were detected. We estimated the flux density limit of < 90/40 mu Jy at 2/9 GHz. The LAT flux upper limits combined with the detection of HESS J0632+057 in the 136-400 TeV energy band by the MAGIC collaboration imply that the VHE spectrum must turn over at energies <136 GeV placing constraints on any theoretical models invoked to explain the gamma-ray emission.
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