What are some Power of the lower Federal court?

Too indefinite a question - not certain what is being asked.

The district courts exercise original jurisdiction over -that is, they are empowered to conduct trials in-the following types of cases:

  • Civil actions arising under the Constitution, laws, and treaties of the United States;
  • Certain civil actions between citizens of different states;
  • Civil actions within the admiralty or maritime jurisdiction of the United States;
  • Criminal prosecutions brought by the United States;
  • Civil actions in which the United States is a party; and
  • Certain other types of cases and controversies