Connections and line bundles

Question

Let $\nabla=d+A$ be a connection over a vector bundle $E$. I try to define a connection over a line bundle:

$$\tilde \nabla_X s = (d+\tilde A)_X s = X.s + tr(A(X))s$$

$$\tilde A=tr(A)$$

Has the associated connection $\tilde \nabla$ a curvature defined by the trace of the curvature of $\nabla$?