In this note we formulate and analyze a hybrid space-time finite element method for the numerical solution of parabolic evolution equations. We combine the more standard variational formulation in Bochner spaces, and a more recent formulation in anisotropic Sobolev spaces using a modified Hilbert transformation. The Galerkin discretization then results in symmetric and positive definite stiffness matrices for both the temporal and spatial derivatives, and a remainder which is in general non-symmetric, but non-negative. We present related error estimates a series of different numerical examples which confirm the theoretical findings.