Measurements of the Cosmological Parameters Omega and Lambda from the First 7 Supernovae at z >= 0.35

We have developed a technique to systematically discover and study high-redshift supernovae that can be used to measure the cosmological parameters. We report here results based on the initial seven of >28 supernovae discovered to date in the high-redshift supernova search of the Supernova Cosmology Project. We find a dispersion in peak magnitudes of sigma_{M_B} = 0.27 this dispersion narrows to sigma_{M_B,corr} = 0.19 after "correcting" the magnitudes using the light-curve "width-luminosity" relation found for nearby (z <= 0.1) type Ia supernovae from the Calan/Tololo survey (Hamuy et al. 1996). Comparing lightcurve-width-corrected magnitudes as a function of redshift of our distant (z = 0.35-0.46) supernovae to those of nearby type Ia supernovae yields a global measurement of the mass density, Omega_M = 0.88^{+0.69}_{-0.60} for a Lambda = 0 cosmology. For a spatially flat universe (i.e., Omega_M +Omega_Lambda = 1), we find Omega_M = 0.94 ^{+0.34}_{-0.28} or, equivalently, a measurement of the cosmological constant, Omega_Lambda = 0.06 ^{+0.28}_{-0.34} (<0.51 at the 95% confidence level). For the more general Friedmann-Lemaitre cosmologies with independent Omega_M and Omega_Lambda, the results are presented as a confidence region on the Omega_M-Omega_Lambda plane. This region does not correspond to a unique value of the deceleration parameter q_0. We present analyses and checks for statistical and systematic errors, and also show that our results do not depend on the specifics of the width-luminosity correction. The results for Omega_Lambda-versus-Omega_M are inconsistent with Lambda-dominated, low density, flat cosmologies that have been proposed to reconcile the ages of globular cluster stars with higher Hubble constant values.