Beneath this tropical spice island's outward tranquility, the arrest of 16 suspected dissidents and a government announcement that it has foiled a coup attempt are arousing fears of political repression.

Residents of Zanzibar, which has semiautonomous status within the Republic of Tanzania, show signs of uncertainty about the government's motives and apprehension that more arrests may be in the offing.

The government declared last weekend that an attempted coup had been thwarted "in the eleventh hour." A public treason trial is expected once investigations are completed. Meanwhile, diplomats here said, the Tanzanian Army is still on "a low-level military alert."

According to these sources, the government moved to arrest the suspected conspirators between June 26 and June 28. About 100 persons initially were rounded up. After questioning, however, all but 16 were released.

Those arrested include four brothers from a wealthy Arab business family, the Battashys, several other Arabs and about a dozen indigenous Africans described as "small" people, such as bus drivers, mechanics or watchmen.

The Battashys, described by their neighbors as "millionaires," are building contractors, large-scale importers and transporters. They are building an enormous two-story concrete house in Zanzibar town, known here as Stone Town. The building is the only new structure to go up there in many years.

Several family members approached in their shop were visibly nervous and refused to answer questions.

"I'm very sorry, but we cannot talk with you," said a spokesman. "You must understand the difficult political situation here."

Other Stone Town residents, conscious of the government's well-organized spy network, were equally unwilling to talk with journalists.

This old town of narrow, twisting streets and tall 19th century buildings with elaborately carved wooden doors seems made for intrigue. Here the 1964 revolution against both British rule and local Arab domination was centered, and the 1971 assassination of Zanzibar's dictatorial leader, Sheik Abeid Karume, was carried out.

Today, observers say, Stone Town is a seat of political opposition to the island's present leader, Aboud Jumbe, who is also Tanzania's vice president.Jumbe has recently lost much support because of a declining economy, food shortages, government mismanagement and corruption. During the past year, wall posters and leaflets occasionally have appeared calling for Jumbe's removal.

Now, with the island's first popular elections scheduled for October, informed sources say, the political opposition is becoming bolder. It includes some old-guard members of the ruling Revolutionary Council. They fear they will be defeated and resent Jumbe's attempts to forge closer ties with the mainland and bring about a limited democratization of the island's political process.

What actually led to the recent arrests is a point of much discussion among Zanzibaris, Tanzanian government officials and diplomats. In an address to the nation last weekend, Jumbe explained that the government had uncovered and infiltrated a plot by "counterrevolutionaries" to overthrow the Zanzibar government by unconstitutional means."

One well-informed source said he has been told by top Zanzibari officials that those arrested "had designed a new flag, drawn up a list of Cabinet members and were trying to get contacts within the Army. They had the idea to use money to buy influence. The Battashys were the only ones with that kind of money. The government has documentary evidence implicating the 16."

However, another reliable source here said that no coup plot existed. Instead, he said, Jumbe received an anonymous letter late last month saying that he was unpopular and should step down in favor of the senior Battashy brother, Abdullah.

Based on this the source said, security forces arrested the Battashys, ransacked their house and found leaflets and private correspondence critical of the government. The next night, the security forces arrested more people and uncovered more antigovernment leaflets and letters.

Other knowledgeable sources also doubt that a coup was imminent and contend that, at the most, the Battashys were discussing plans to bankroll opposition candidates in the forthcoming elections.

One Tanzanian official, unsympathetic to Jumbe, accused the Zanzibari leader of using "Idi Amin tactics," a reference to the former Ugandan dictator's penchant for claiming a coup or invasion whenever faced with political or economic troubles at home.

For now, Zanzibaris themselves seem resigned to waiting for the trial to see what real evidence the government will produce.