I am putting in new service at the house. 150 amp service from 100 amp. What size service entrance cable do I need

Looks like you could use this Wire sizes, gauges, for breakers

Don't bother with 150 amps. The cost difference between that and 200 is almost nil.
150A services are just not worth it.

Question. Why install 150 Amp service? If you are going through the pain of upgrading your service, consider going to the 200 amp level.