We report the measurement of gamma gamma to eta_c(1S), eta_c(2S) to eta pi+ pi- with eta decays to gamma rho and eta pi+ pi- using 941 fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. The eta_c(1S) mass and width are measured to be M = [2984.6pm0.7 (stat.)pm2.2 (syst.)] MeV/c^{2} and Gamma = [30.8^{+2.3}_{-2.2}~(stat.) pm 2.5~(syst.)] MeV, respectively. First observation of eta_c(2S) to eta pi+ pi- with a significance of 5.5sigma including systematic error is obtained, and the eta_c(2S) mass is measured to be M = [3635.1pm3.7~(stat.)pm2.9~(syst.)] MeV/c^{2}. The products of the two-photon decay width and branching fraction (B) of decays to etapi+ pi- are determined to be Gamma_{gamma gamma}B = [65.4pm2.6~(stat.)pm6.9~(syst.)] eV for eta_c(1S) and [5.6^{+1.2}_{-1.1}~(stat.)pm1.1~(syst.)] eV for eta_c(2S). A new decay mode for the eta_c(1S) to etaf_0(2080) with f_0(2080) to pi+ pi- is observed with a statistical significance of 20sigma. The f_0(2080) mass and width are determined to be M = [2083^{+63}_{-66}~(stat.)pm 32~(syst.)] MeV/c^{2} and Gamma = [178^{+60}_{-178}~(stat.) pm 55~(syst.)] MeV. The cross sections for gamma gamma to eta pi+ pi- and etaf_{2}(1270) are measured for the first time.
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