Stocks trimmed gains modestly on Tuesday after June homebuilder sentiment fell by the sharpest amount since the height of the financial crisis as a homebuyer tax credit expired.

* Indexes saw support from earlier data showing inflation continued to be under control and as the euro rose on strong demand at European debt auctions.

* The Dow Jones industrial average <.DJI> rose 82.76 points, or 0.81 percent, to 10,273.65. The Standard & Poor's 500 Index <.SPX> added 9.26 points, or 0.85 percent, to 1,098.89. The Nasdaq Composite Index <.IXIC> gained 25.09 points, or 1.12 percent, to 2,269.05.

(Reporting by Leah Schnurr; editing by Jeffrey Benkoe)