* Initial claims rise more than expected
* ISM rises, but shy of expectations
* Google dividend takes effect
* Indexes off: Dow 0.07 pct, S&P 0.11 pct, Nasdaq 0.37 pct
(Updates to open, adds ISM data)
NEW YORK, April 3 (Reuters) - U.S. stocks were little changed on Thursday, with the S&P 500 holding near its recent record, as investors exercised restraint before Friday's employment report and data suggested modest improvement in the economy.
Initial weekly claims for state unemployment benefits increased 16,000 to a seasonally adjusted 326,000, above the 317,000 forecast. Claims for the previous week were revised to show 1,000 fewer applications than earlier reported and the underlying trend continued to point to some strength in the labor market.
The Institute for Supply Management said its services sector index rose to 53.1 in March, slightly below expectations for a read of 53.5 but comfortably ahead of the February read of 51.6.
Investors may be hesitant to make big bets ahead of Friday's payrolls report, as they look for evidence that recent weather-related weakness in the economy has passed. However, while recent reports have shown a recovery from earlier this year, when a harsh winter hurt some data, they have not markedly improved over last year.
"The information we've gotten so far today is a little bit on the light side with respect to leading us towards bullishness, but not enough to make us run screaming 'sell' down the halls," said Kim Forrest, senior equity research analyst, Fort Pitt Capital Group in Pittsburgh.
"This year is the same as last year and we are disappointed ultimately because we would like to see some positive change."
Other data showed the trade gap widened 7.7 percent to $42.3 billion, the largest since September, as exports fell to their lowest in five months in a further sign that economic growth had slowed in the first quarter.
The Dow Jones industrial average fell 11.37 points or 0.07 percent, to 16,561.63, the S&P 500 lost 2.1 points or 0.11 percent, to 1,888.8 and the Nasdaq Composite dropped 15.756 points or 0.37 percent, to 4,260.7.
The S&P 500 now consists of 501 stocks, as the index now includes both Google Inc's Class A and Class C shares in the wake of the company's special dividend. Class A shares rose 2.8 percent to $584 while Class C shares gained 2.5 percent to $581.26.
Gilead Sciences Inc said late Wednesday a trial of its hepatitis C drug sofosbuvir, sold under the brand name Sovaldi in the United States, showed the drug was safe and effective in treating Japanese patients infected with a common form of the virus. However, its shares dipped 1.8 percent to $72.63.
Vivus Inc slumped 7.8 percent to $5.70 after Piper Jaffray cut its rating on the stock to "underweight" from "neutral."
(Editing by Bernadette Baum)