Narrow-line Seyfert 1 galaxies have been identified by the Fermi Gamma-Ray Space Telescope as a rare class of \gamma -ray emitting active galactic nuclei ( AGN ) .
The lowest-redshift candidate among them is the source 1H 0323 + 342 .
Here we present quasi-simultaneous Gemini near-infrared and Keck optical spectroscopy for it , from which we derive a black hole mass based on both the broad Balmer and Paschen emission lines .
We supplement these observations with a NuSTAR X-ray spectrum taken about two years earlier , from which we constrain the black hole mass based on the short timescale spectral variability .
Our multiwavelength observations suggest a black hole mass of \sim 2 \times 10 ^ { 7 } M _ { \odot } , which agrees well with previous estimates .
We build the spectral energy distribution and show that it is dominated by the thermal and reprocessed emission from the accretion disc rather than the non-thermal jet component .
A detailed spectral fitting with the energy-conserving accretion disc model of Done et al .
constrains the Eddington ratio to L / L _ { Edd } \sim 0.5 for a ( non-rotating ) Schwarzschild black hole and to L / L _ { Edd } \sim 1 for a Kerr black hole with dimensionless spin of a ^ { \star } = 0.8 .
Higher spin values and so higher Eddington ratios are excluded , since they would strongly overpredict the observed soft X-ray flux .