Subspace $\ell^2$ is of first category 
Let $\ell^2$ be the Hilbert space of square summable sequences, and $\mathcal{H}$ be the subspace consisting of sequences $\{x_n\}$ with $\sum_{n=1}^\infty n^2|x_n|^2<\infty$
  Show that $\mathcal{H}$ is of the first category.

I unsure how to start this problem.  

Hint: Consider $E_M=\{(x_n)\in l^2: \sum n^2x_n^2\le M\}.$ Show $E_M$ is closed in $l^2.$ (Fatou's lemma). Then show $E_M$ has no interior.
