  We present results from the first radiation non-ideal magnetohydrodynamics
(MHD) simulations of low-mass star cluster formation that resolve the
fragmentation process down to the opacity limit. We model 50~M$_\odot$
turbulent clouds initially threaded by a uniform magnetic field with strengths
of 3, 5 10 and 20 times the critical mass-to-magnetic flux ratio, and at each
strength, we model both an ideal and non-ideal (including Ohmic resistivity,
ambipolar diffusion and the Hall effect) MHD cloud. Turbulence and magnetic
fields shape the large-scale structure of the cloud, and similar structures
form regardless of whether ideal or non-ideal MHD is employed. At high
densities ($10^6 \lesssim n_{\rm H} \lesssim 10^{11}$~cm$^{-3}$), all models
have a similar magnetic field strength versus density relation, suggesting that
the field strength in dense cores is independent of the large-scale
environment. Albeit with limited statistics, we find no evidence for the
dependence of the initial mass function on the initial magnetic field strength,
however, the star formation rate decreases for models with increasing initial
field strengths; the exception is the strongest field case where collapse
occurs primarily along field lines. Protostellar discs with radii $\gtrsim
20$~au form in all models, suggesting that disc formation is dependent on the
gas turbulence rather than on magnetic field strength. We find no evidence for
the magnetic braking catastrophe, and find that magnetic fields do not hinder
the formation of protostellar discs.
