In the case Gitlow v. New York, Gitlow argued that his First Amendment rights were being violated? that he couldn't be convicted of the same crime twice? that his Sixth Amendment rights guaranteed him the right to a jury? or that he couldn't be jailed without being charged with a crime?

The correct answer is:

His First Amendment rights were being violated.

Benjamin Gitlow was convicted of violating a New York law criminalizing the advocacy of overthrowing the government for handing out literature advocating the establishment of socialism in the United States.

Gitlow's defense attempt to declare the publication of the Left Wing Manifesto as an expression of historical analysis rather than an act of practical advocacy was unsuccessful. The Supreme Court confirmed Gitlow's conviction, and for the first time held that the First Amendment applied to the states by virtue of the Due Process Clause of the Fourteenth Amendment.