Mass of a lattice (awaiting review)

For an integral lattice $L$, the mass of $L$ is the weighted sum $$ \sum_{\Lambda} \frac{1}{\# \text{Aut} (\Lambda)} $$ where the sum runs over all isometry classes of lattices $\Lambda$ in the same genus as $L$. Here $\text{Aut}(\Lambda)$ denotes the automorphism group of $\Lambda$.