Let \(A\) be the first Weyl algebra over the field of complex numbers. The authors study simple \(A\)-modules with a view to finding connections with Ore subsets of \(A\). The results are too technical to be stated here, but for the most part they are concerned with the composition factors of modules of the form \(A/Ax\) for a non-zero element \(x\) of \(A\), and give ways of calculating the number of times a given simple module occurs in a composition series for \(A/Ax\).