With the Democratic National Convention in New York less than two weeks away, President Carter's job rating by the voters has sunk to new lows. Carter's overall rating on the job he is doing in the White House is now 77 to 22 percent negative. His previous low of 74 to 25 percent negative, recorded last October, had been the lowest recorded for a president in modern political history.

Carter's troubles are evident in the ratings the electorate gives him across the board, according to this lastest ABC News-Harris Survey of 1,458 likely voters nationwide. The polling was done July 18-21.

By 86 to 12 percent, the president receives negative marks on his "handling of the economy." His previous low on this key dimension took place early last October, when his rating was 84 to 14 percent negative.

By an even higher 89 to 10 percent, he is given a negative rating on "keeping inflation under control." His previous low was 86 to 12 percent negative last October.

By 87 to 11 percent, he comes up with negative marks on his "handling of unemployment," up from a comparable 81 to 16 percent negative rating in June.

In the area of foreign policy, a source of strength for Carter earlier this year, the bottom appears have dropped out of public confidence:

By 79 to 19 percent the voters give Carter negative marks on his handling of the situation in Iran, down from 74 to 24 percent negative last month, and sharply down from the 66 to 32 percent positive rating accorded him on the hostage issue last December. This is a complete reversal of the people's appraisal of the Carter performance on Iran, a negative swing of 47 points in seven months.

By an even greater 83 to 16 percent, a sizable majority gives Carter negative marks on the way he has handled the Cuban refugee problem. The influx of well over 100,000 Cubans into the United States has caused particular bitterness among blacks, Hispanics and white southerners. The central concern is that a time when unemployment and inflation are both high is not the right moment to try to absorb so many refugees and also find them gainful employment.

By a massive 82 to 17 percent, a majority of the voters have therefore concluded that Carter does not deserve positive marks in his handling of foreign policy matters. Back in December, a 51 to 47 percent majority gave Carter a positive rating on his stewardship with regard to foreign affairs.

It is important to point out that this has been a volatile year as far as public opinion is concerned, and that Ronald Reagan, who now holds a 28-point lead over Carter, may be just as capable of blowing his lead as Carter did his similar lead over Gerald R. Ford in 1976.