The impurity paramagnetic ion, Cu2+ substitutes Al in the SrLaAlO4 single crystal lattice, this results in a CuO6 elongated octahedron, and the resulting measured g-factors satisfy four-fold axes variation condition. The aggregate frequency width of the electron spin resonance with the required minimum level of impurity concentration has been evaluated in this single crystal SrLaAlO4at 20 millikelvin. Measured parallel hyperfine constants, A∥Cu, were determined to be -155.7 × 10-4 cm-1, - 163.0 × 10-4 cm-1, - 178.3 × 10-4 cm-1 and -211.1 × 10-4 cm-1 at 9.072 GHz (WGH4,1,1) for the nuclear magnetic quantum number MI = +3/2 ,+1/2 ,-1/2 , and-3/2 respectively. The anisotropy of the hyperfine structure reveals the characteristics of the static JahnTeller effect. The second-order-anisotropy term, ≈ ( spin-orbit coupling/10Dq )2, is significant and cannot be disregarded, with the local strain dominating over the observed Zeeman-anisotropy-energy difference. The Bohr electron magneton, - = 9.23 × 10-24JT-1, (within -0.43% so-called experimental error) has been found using the measured spin-Hamiltonian parameters. Measured nuclear dipolar hyperfine structure parameter P- = 12.3 × 10-4 cm-1 shows that the mean inverse third power of the electron distance from the nucleus is 〈rq -3〉 ≲ 5.23 a.u. for Cu2+ ion in the substituted Al3+ion site assuming nuclear electric quadruple moment Q = -0.211 barn.