  Using the Ratios Conjecture, we write down precise formulas with lower order
terms for the one and the two level densities of zeros of quadratic Dirichlet
$L$--functions over function fields. We denote the various terms arising as
Type-$0$, Type-I and Type-II contributions. When the support of the Fourier
transform of the test function is sufficiently restricted, we rigorously
compute the Type-$0$ and Type-I terms and confirm that they match the
conjectured answer. When the restrictions on the support are relaxed, our
results suggest that Type-II contributions become important in the two level
density.
