For a sample of 4378 nearby spiral and S0 galaxies, Yu & Ho used Fourier analysis of Sloan Digital Sky Survey images to show that the strengths of the spiral arms and the pitch angles of the arms are inversely correlated with central concentration. In the current study, we search for trends in the Yu & Ho spiral arm parameters with environment and specific star formation rate (sSFR). When comparing galaxies with similar concentrations, we do not find a significant difference in the arm strengths or pitch angles of spiral galaxies in clusters compared to field galaxies. When differences in concentration are taken into account, we also find no significant difference in the parameter f3 for cluster spirals compared to field spirals, where f3 is the normalized m = 3 Fourier amplitude. When concentration is held fixed, both arm strength and pitch angle are correlated with sSFR, but f3 is not. These relations support the suggestion by Davis et al. of a “fundamental plane” of spiral structure involving pitch angle, bulge stellar mass, and gas surface density. We discuss these results in terms of theories of spiral arm production and quenching in galaxies. To aid comparison with earlier studies based on Galaxy Zoo, we explore how the Yu & Ho parameters relate to similar parameters measured by Galaxy Zoo (i.e., f3 versus the number of arms, pitch angle versus winding parameter, and concentration versus bulge class).