The J = 0 infrared spectrum of methoxy is theoretically calculated for the ground (X) over tilde E-2 state using a quartic potential energy force field, and the quadratic dipole moment expansion is calculated ab initio at the CCSD(T) level of theory and cc-pVTZ basis. Writing these expansions with vibronic operators whose symmetry properties are defined with respect to C-3v rotation greatly simplifies these calculations. With minor adjustments to the force field, excellent agreement with experiment is found for both the transition energies of CH3O and those of CD3O. The role of Jahn-Teller Teller and Fermi coupling is illustrated by scaling these terms by a parameter 5 that varies from 0 to 1. Plotting the eigenvalues as a function of delta yields a correlation diagram connecting the harmonic eigenvalues to those of the fully coupled problem. The spectrum for CH3O is determined using a combination of Davidson and Lanczos iteration schemes. The spectral features are found to be dominated by Jahn-Teller effects, but direct Fermi coupling and indirect potential couplings have important roles. The origin of the complexities in the CH stretch region are discussed.