Alexander hamilton argued that the federal government held what powers beyond its delegated authority?

Hamilton believed that the federal government had powers to do whatever was "necessary and proper" in exercising leadership beyond its specifically enumerated powers.

A key example was Hamilton's argument for the creation of a national bank, which was not specifically stipulated by the Constitution.  Hamilton's argument was based on the "necessary and proper" clause of Article I, Section 8, of the United States Constitution.  After enumerating a number of the powers of Congress, including borrowing money, coining money, regulating commerce, etc, Section 8 of Article I closes with by saying Congress shall have power "to make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof."  

Hamilton favored a loose interpretation of the Constitution -- in other words, that the Constitution allows for anything that is not strictly forbidden in what it has expressly stated.  A national bank was not strictly listed as something Congress could establish, but there was nothing in the Constitution to prohibit it.  And the "necessary and proper" clause gave leeway to create it.

Overall, Hamilton favored a stronger federal government than did some of his peers among the founding fathers.