  In this paper, we report a detailed investigation of the multiwavelength
properties of a newly detected gamma-ray pulsar, PSR J2021+4026, in both
observational and theoretical aspects. We firstly identify an X-ray source in
the XMM-Newton serendipitous source catalogue, 2XMM J202131.0+402645, located
within the 95% confidence circle of PSR J2021+4026. With an archival Chandra
observation, this identification provides an X-ray position with arcsecond
accuracy which is helpful in facilitating further investigations. Searching for
the pulsed radio emission at the position of 2XMM J202131.0+402645 with a 25-m
telescope at Urumqi Astronomical Observatory resulted in null detection and
places an upper-limit of 0.1~mJy for any pulsed signal at 18~cm. Together with
the emission properties in X-ray and gamma-ray, the radio quietness suggests
PSR J2021+4026 to be another member of Geminga-like pulsars. In the radio sky
survey data, extended emission features have been identified in the gamma-ray
error circle of PSR J2021+4026. We have also re-analyzed the gamma-ray data
collected by FERMI's Large Area Telescope. We found that the X-ray position of
2XMM J202131.0+402645 is consistent with that of the optimal gamma-ray timing
solution. We have further modeled the results in the context of outer gap model
which provides us with constraints for the pulsar emission geometry such as
magnetic inclination angle and the viewing angle. We have also discussed the
possibility of whether PSR J2021+4026 has any physical association with the
supernova remnant G78.2+2.1 (gamma-Cygni).
