Using simple stellar population synthesis , we model the bulge stellar contribution in the optical spectrum of a narrow-line Seyfert 1 galaxy RE J1034+396 .
We find that its bulge stellar velocity dispersion is 67.7 \pm 8 km s ^ { -1 } .
The supermassive black hole ( SMBH ) mass is about ( 1 - 4 ) \times 10 ^ { 6 } M _ { \odot } if it follows the well-known M _ { BH } - \sigma _ { * } relation found in quiescent galaxies .
We also derive the SMBH mass from the H \beta second moment , which is consistent with that from its bulge stellar velocity dispersion .
The SMBH mass of ( 1 - 4 ) \times 10 ^ { 6 } M _ { \odot } implies that the X-ray quasi-periodic oscillation ( QPO ) of RE J1034+396 can be scaled to a high-frequency QPO at 27-108 Hz found in Galactic black hole binaries with a 10 M _ { \odot } black hole .
With the mass distribution in different age stellar populations , we find that the mean specific star formation rate ( SSFR ) over past 0.1 Gyr is 0.0163 \pm 0.0011 Gyr ^ { -1 } , the stellar mass in the logarithm is 10.155 \pm 0.06 in units of solar mass , and the current star formation rate is 0.23 \pm 0.016 ~ { } M _ { \odot } ~ { } yr ^ { -1 } .
RE J1034+396 does not follow the relation between the Eddington ratio and the SSFR suggested by Chen et al. , although a larger scatter in their relation .
We also suggest that about 7.0 % of the total H \alpha luminosity and 50 % of the total [ O ii ] luminosity come from the star formation process .