condition for the Dirac delta function to be in Hilbert space

Question

I have a problem to show $$ \delta\in\mathcal{H}^s(\mathbb{R}^n) \iff s<-\dfrac{n}{2}. $$ where $ \mathcal{H}^s(\mathbb{R}^n)= \{f\in\mathcal{S}'(\mathbb{R}^n): \Vert(1+\vert\xi\vert^2)^{s/2} \mathcal{F}[f]\Vert_{L_p(\mathbb{R}^n)} \}$, for $ \mathcal{F} $ the Fourier transform. Here $ \mathcal{F}\delta=(2\pi)^{-n/2} $.

Now,$ \delta\in\mathcal{H}^s(\mathbb{R}^n)$ means $$ \int_{\mathbb{R}^n}\vert (1+\vert\xi\vert^2)^{s/2}(2\pi)^{-n/2}\vert d\xi $$ But how can I proceed from here and on?