Let $\Sigma = \{0,1\}$, and consider the language $$L = \{\langle M \rangle \mid M \text{ is a TM and } L(M) \text{ is a subset of } Σ^* \text{ and all strings in this set have an even number of 1s}\}.$$
I think $L$ is undecidable. But I am stuck on proving it. I think it is equivalent to prove $L = \{\langle M \rangle \mid M \text{ is a TM and } L(M) \text{ is a specific set with an even number of 1s}\}$ is undecidable. How can I do some reduction for it?