The equation-of-motion coupled cluster method for excited electronic applied to study the structure and selected properties of the first excited singlet state of s-tetrazine. Adiabatic S-1<--S-0 excitation energies obtained with large basis sets containing up to 270 functions are uniformly somewhat above the experimental 0-0 value of 2.238 eV, but nevertheless are the most accurate calculations reported to date for this quantity. The equilibrium geometry of S-1 predicted in this study is in excellent agreement with another high-level calculation, and moreover is quantitatively consistent with both the intensity of vibrational progressions observed in absorption and measured rotational constants for S-1. The EOMEE-CC harmonic force field of S-1 is the first to satisfactorily describe the low frequency in-plane b(3g) bending mode, notably its marked reduction in frequency upon excitation and characteristic positive anharmonicity. Both of these effects are due to a strong second-order Jahn-Teller interaction between S1 and the nominal S-2((1)A(u)) state, which is also investigated superficially in this work. Finally, results presented for the static dipole polarizabilies of the S-1 state join others in calling for a reinvestigation of the experimentally determined parameters.