We report on a spectroscopic determination of the atmospheric parameters and chemical abundance of the parent star of the recently discovered transiting planet TrES-2. A detailed LTE analysis of a set of Fe I and Fe II lines from our Keck spectra yields T_(eff) = 5850 ± 50 K, log g = 4.4 ± 0.1, and [Fe/H] = -0.15 ± 0.10. Several independent checks (e.g., additional spectroscopy, line-depth ratios) confirm the reliability of our spectroscopic T_(eff) estimate. The mass and radius of the star, needed to determine the properties of the planet, are traditionally inferred by comparison with stellar evolution models using T_(eff) and some measure of the stellar luminosity, such as the spectroscopic surface gravity. We apply here a new method in which we use instead of log g the normalized separation a/R_* (related to the stellar density), directly measurabele from the light curves of transiting planets with much greater precision. With the a/R_* value from the light-curve analysis of Holman and coworkers and our T_(eff) estimate, we obtain M_* = 0.980 ± 0.062 M_☉ and R_* = 1.000^(+0.036)_(-0.033) R_☉, and an evolutionary age of 5.1^(+2.7)_(-2.3) Gyr, in good agreement with other constraints (Ca II H and K line cores, lithium abundance, and rotation). The new stellar parameters yield improved values for the planetary mass and radius of M_p = 1.198 ± 0.053 M_J and R_p = 1.220^(+0.045)_(-0.042) R_J, confirming that TrES-2 is the most massive among the currently known nearby (d ≲ 300 pc) transiting hot Jupiters. The surface gravity of the planet, log g_p = 3.299 ± 0.016, can be derived independently of the knowledge of the stellar parameters (i.e., directly from observations), and with a very high precision rivaling that of the best known double-lined eclipsing binaries
