  We examine the effect of multilevels on decoherence and dephasing properties
of a quantum system consisting of a non-ideal two level subspace, identified as
the qubit and a finite set of higher energy levels above this qubit subspace.
The whole system is under interaction with an environmental bath through a
Caldeira-Leggett type coupling. The model interaction we use can generate
nonnegligible couplings between the qubit states and the higher levels upto
$N\sim 10$. In contrast to the pure two-level system, in a multilevel system
the quantum information may leak out of the qubit subspace through nonresonant
as well as resonant excitations induced by the environment. The decoherence
properties of the qubit subspace is examined numerically using the master
equation formalism of the system's reduced density matrix. We numerically
examine the relaxation and dephasing times as the environmental frequency
spectrum, the environmental temperature, and the multilevel system parameters
are varied. We observe the influence of all energy scales in the noise spectrum
on the short time dynamics implying the dominance of nonresonant transitions at
short times. The relaxation and dephasing times calculated, strongly depend on
$N$ for $4< N<10$ and saturate for $10 <N$. We also examine double degenerate
systems with $4 \le N$ and observe a strong suppression (almost by two orders
of magnitude) of the low temperature relaxation and dephasing rates.
  An important observation for $4 \le N$ in doubly degenerate energy
configuration is that, we find a strong suppression of the RD rates for such
systems relative to the singly degenerate ones. These results are also compared
qualitatively with the relaxation rates found from the Fermi Golden Rule.
