Isomerization between the cis and trans conformers of the S1 state of acetylene is studied using a reduced dimension discrete variable representation (DVR) calculation. Existing DVR techniques are combined with a high accuracy potential energy surface and a kinetic energy operator derived from FG theory to yield an effective but simple Hamiltonian for treating large amplitude motions. The spectroscopic signatures of the S1 isomerization are discussed, with emphasis on the vibrational aspects. The presence of a low barrier to isomerization causes distortion of the trans vibrational level structure and the appearance of nominally electronically forbidden A1A2X1g+ transitions to vibrational levels of the cis conformer. Both of these effects are modeled in agreement with experimental results, and the underlying mechanisms of tunneling and state mixing are elucidated by use of the calculated vibrational wavefunctions.