A method to determine the full structure of the space of local operators of massive integrable field theories, based on the form factor bootstrap approach is presented. This method is applied to the integrable perturbations of the Ising conformal point. It is found that the content of local operators can be expressed in terms of fermionic sum representations of the characters \c(q) of the Virasoro irreducible representations of the minimal model \M_{3,4}. The space of operators factorises into chiral components as Z=\sum \c(q) \c(\q), but with the relation \q=q^{-1}.
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