Hi, can anyone help with the following?

Given the Language L\ = \{\sigma1^{3k}}\in \{0,1\}^* \mid \sigma\ codes\ a\ Turing\ Machine\ M\ which\ on\  insert\ \sigma1^{3k}}\ halts\ within\ at\ most\ 2^k\ steps\ without\ accepting\ \}


Show that  L \notin P and find a function T(n) such that  L \in Time(T(n))


This the first time I have been asked to show a language is not in some class, and I'm quite stumped.