For each pseudo-Anosov map, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$. This invariant is defined by interaction between Thurston norm and dilatation of pseudo-Anosov map. We will develop a few nice properties of our invariant and give a few examples to show it can be nontrivial. These nontrivial examples give negative answer to a question asked by McMullen.