The powers denied to Congress are enumerated in Article 1, Section 9 of the Constitution of the United States. A key provision necessary for passing the original Constitution was a compromise between the free and slave states. In that section of the Constitution, Congress was prevented from interfering with the slave trade until at least 1808.
Other powers denied to Congress include suspending the writ of habeas corpus, except in the event of rebellion or invasion. This prevents a person from being held against his will without just cause and judicial oversight. Congress is also prevented from enacting any ex post facto laws or passing a bill of attainder.
Ex post facto laws are enacted retroactively and are designed to penalize someone for something that is not illegal at the time the act is committed. A bill of attainder is a law designed to have a negative impact on a single person or a group of people.
Congress is denied the power to tax goods that are shipped from one state to another. Congress cannot give a commercial advantage to one state over another. Originally, the Constitution precluded Congress from levying an income tax. A subsequent amendment to the Constitution granted this power to Congress.