  The main objective of this article is to study the asymptotic behavior of
Salie sums over arithmetic progressions. We deduce from our asymptotic formula
that Salie sums possess a bias of being positive. The method we use is based on
Kuznetsov formula for modular forms of half integral weight. Moreover, in order
to develop an explicit formula, we are led to determine an explicit orthogonal
basis of the space of modular forms of half integral weight.
