  We report an inelastic neutron scattering (INS) study under a magnetic field
on the frustrated molecular spin cluster $V_{15}$. Several field-dependent
transitions are observed and provide a comprehensive understanding of the
low-energy quantum spin states. The energy gap $2 \Delta_{0}\approx 27(3)\mu$eV
between the two lowest $S=1/2$ Kramers doublets is unambiguously attributed to
a symmetry lowering of the cluster. The INS data are mapped onto an S=1/2
Antiferromagnetic Heisenberg triangle with scalene distortion. A quantitative
description of the wavefunction mixing within the ground state is derived.
