Olympic arts, usually on the sidelines, may turn heads in L.A.

The hidden Olympics - the Olympic Arts Festival, which shyly accompanies the Summer Games every four years - appears to be turning more heads this round than any other since the modern games began.

The modern Olympics were designed to gather the best in the arts, as well as in sport, as in the ancient Olympics of the Greeks. But from the beginning, in 1896, the athletic competition has so overshadowed the cultural events that few Olympic spectators have even noticed the arts were there.

This summer in Los Angeles may be different. The arts may break with tradition and make a bigger splash than the 10-meter-board divers.

One not-so-subtle indication:

The third week in January, just after the festival schedule was announced, some 74,500 people called the Olympic headquarters for tickets or brochures to the arts events. Another 8,600 tried and couldn't get through the lines. The sacks of mail have yet to be tallied by the computer.

So yes, says director of the festival Robert J. Fitzpatrick, this will be the most attention-getting arts festival the Olympics has ever had.

Part of the reason is simply the popularity of the Olympics, which this year look to be the world's best-selling sports event ever.

Mr. Fitzpatrick describes a ''sense of event'' he wants the festival to cultivate around the games: ''That sense that 1984 is here, and in the summer of 1984, half the human race will focus on Los Angeles.''

The Olympics, Fitzpatrick muses, are the only ''truly international event, short of nuclear war.'' And, so far, the Los Angeles games have not been tainted by the political controversy that has corrupted recent Olympics.

''We really do want to go back to the spirit of the ancient Greeks, when wars stopped for the games.''

A case in point: When China cut off all cultural exchange with the United States last April ago because the US gave asylum to defecting tennis star Hu Na, Chinese officials immediately called up Fitzpatrick to say the arts festival would not be affected.

This is the first time the People's Republic of China has participated in the Olympics, and Fitzpatrick has been impressed with the excitement there. ''This is a major Chinese policy statement and cultural statement,'' he says. He recalls walking through a marketplace in Chengdu, China, while Chinese left their market stalls to follow after him calling, ''Hello, Olympic.''

Fitzpatrick's office is a sort of cultural bunker under the vast, cavernous ceilings of the old helicopter hangar that houses the Olympic organizing effort.

Moving pads hang from the jerry-built walls, and posters, masks, and flags are tacked up around the room. The phone rings with a call from Italy. Aides bustle by.

Perhaps the most massive project slated for the festival is an avant-garde opera by Robert Wilson with the avant-garde title, ''CIVIL warS: a tree is best measured when it is down.'' Parts of the opera have been produced abroad, but the Olympic festival will represent its premiere intact. Negotiations are under way for the the German Air Force to fly the cast and equipment to Los Angeles.

Just one example of the cosmopolitan character of the festival: A French theatrical company, Le Theatre du Soleil, will perform Shakespeare's ''Richard II'' in French, using the style of the formal, white-faced, Japanese Kabuki theater.

Fitzpatrick has been on two televised debates in Italy over bringing to Los Angeles two ancient Greek bronzes discovered off the coast of Italy. Italian Prime Minister Bettino Craxi and three other cabinet ministers met a week ago and decided against it.

This is one of Fitzpatrick's few disappointments in putting together a 400 -event festival, ranging from classical music and art exhibitions to country-and-western concerts. Another is the nonparticipation of the Soviet Union, which dropped negotiations in September.

Fitzpatrick says the Olympics will get $21 million worth of festival for $10 million. He has tried to use his festival budget as seed money for other financing. For the Royal Opera of Covent Garden, for example, the arts festival only put up 10 percent of the cost of bringing the company London to Los Angeles.

In a city that didn't get its first piano until 1883, he points out, ''this festival is a sort of coming of age.''