NEW YORK, Feb 28 (Reuters) - Former U.S. vice presidential candidate Sarah Palin asked a U.S. court on Monday for a new trial after losing her defamation case against the New York Times (NYT.N) earlier this month, and requested that the judge overseeing the case be disqualified. Palin's attorneys said last week they would take those steps because several jurors received push notifications on their cellphones before deliberations were over about U.S. District Judge Jed Rakoff's decision to dismiss the case regardless of their verdict.