Context :

Aims : We aim to characterize the broadband emission from 2FGL J2001.1+4352 , which has been associated with the unknown-redshift blazar MG4 J200112+4352 .
Based on its gamma-ray spectral properties , it was identified as a potential very high energy ( VHE ; E > 100 GeV ) gamma-ray emitter .
We investigate whether this object is a VHE emitter , characterize its gamma-ray spectrum , and study the broadband emission within the one-zone synchrotron self-Compton ( SSC ) scenario , which is commonly used to describe the emission in blazars .
Moreover , we also intend to determine the redshift of this object , which is a crucial parameter for its scientific interpretation .

Methods : The source was observed with MAGIC first in 2009 and later in 2010 within a multi-instrument observation campaign .
The MAGIC observations yielded 14.8 hours of good quality stereoscopic data .
Besides MAGIC , the campaign involved , observations with Fermi -LAT , Swift -XRT/UVOT , the optical telescopes KVA , Goddard Robotic Telescope , Galaxy View observatory , Crimean Astrophysical observatory , St. Petersburg observatory , and the Owens Valley Radio Observatory .
The object was monitored at radio , optical and gamma-ray energies during the years 2010 and 2011 .
We characterize the radio to VHE spectral energy distribution and quantify the multiband variability and correlations over short ( few days ) and long ( many months ) timescales .
We also organized deep imaging optical observations with the Nordic Optical Telescope in 2013 to determine the source redshift .

Results : The source , named MAGIC J2001+439 , is detected for the first time at VHE with MAGIC at a statistical significance of 6.3 \sigma ( E > 70 GeV ) during a 1.3-hour long observation on 2010 July 16 .
The multi-instrument observations show variability in all energy bands with the highest amplitude of variability in the X-ray and VHE bands .
Besides the variability on few-day timescales , the long-term monitoring of MAGIC J2001+439 shows that , the gamma-ray , optical , and radio emissions gradually decreased on few-month timescales from 2010 through 2011 , indicating that at least some of the radio , optical and gamma-ray emission is produced in a single region by the same population of particles .
We also determine for the first time the redshift of this BL Lac object through the measurement of its host galaxy during low blazar activity .
Using the observational evidence that the luminosities of BL Lac host galaxies are confined to a relatively narrow range , we obtain z = 0.18 \pm 0.04 .
Additionally , we use the Fermi -LAT and MAGIC gamma-ray spectra to provide an independent redshift estimation , z = 0.17 \pm 0.10 .
Using the former ( more accurate ) redshift value , we adequately describe the broadband emission with a one-zone SSC model for different activity states and interpret the few-day timescale variability as produced by changes in the high-energy component of the electron energy distribution .

Conclusions :