Why did the Federalists oppose the Louisiana Purchase?

The Federalists opposed the Louisiana Purchase, as it was an expression of Jefferson's radical Republican ideology. He believed that the purchase, and the inevitable western expansion that would follow, would strengthen his ideal of a nation where ultimate sovereignty resides with the states. The expansion of the United States into the West would serve to undermine the political authority of Jefferson's Federalist opponents, whose main power base was among the banking and commercial elites of the East Coast.
Federalists were concerned that the Louisiana Purchase would undermine their whole project of centralizing government power, a project they felt was essential to establishing the United States as a serious player on the international stage. As well as giving more power to the individual states, the purchase would shift the center of gravity in the American economy from commerce and banking towards agriculture. This is precisely what Jefferson hoped for; he believed that the tradition of republican liberty, as set down in the Declaration of Independence, required for its protection the existence of a class of landowners with an attachment to their native soil. Land was the ultimate source of wealth for Jefferson, hardly a surprising attitude when one considers that Jefferson himself was a substantial owner of land. His vision, both political and economic, was diametrically opposed to that of the Federalists. The Louisiana Purchase would add greater substance to that vision, and both Jefferson and his Federalist opponents knew it.