  An extended multi-hadron operator is developed to extract the spectra of
irreducible representations in the finite volume. The irreducible
representations of the cubic group are projected using a coordinate-space
operator. The correlation function of this operator is computationally
efficient to extract lattice spectra. In particular, this new formulation only
requires propagator inversions from two distinct locations, at fixed physical
separation. We perform a proof-of-principle study on a $24^3 \times 48$ lattice
volume with $m_\pi\approx 900$~MeV by isolating the spectra of $A^+_1$, $E^+$
and $T^+_2$ of the $\pi\pi$ system with isospin-2 in the rest frame.
