The Fairfax County Board of Supervisors initialed an investigation yesterday after learning that the County Council of the Arts accepted a 1 percent interest in a cable television company competing for a Fairfax franchise in exchange for advice on arts programming.

"It was just a very stupid thing for them to do," said Supervisor Martha V. Pennino (D-Centreville) on learning that the arts council, which receives county funds, accepted 1,000 shares of stock in Trans County Cable Communications Inc., a subsidiary of Storer Broadcasting Co. Trans County is among 23 companies that have expressed interest in bidding on Fairfax's two lucrative cable TV franchises.

"I'm sure they did it in innocence and good faith, but . . . it puts the governing body in a conflict-of-interest situation," Pennino said.

Officials of Trans County confirmed that they had granted the nonprofit organization a 1 percent stock interest in return for it advice on designing arts programming. They stressed that both they and the council's board of directors had agreed that they would engage in no lobbying activities when the supervisors make their decision on the franchise award early next year.

"The ony way there could be any possibility of influence would be by designing a superb package," said Frederick Lee Ruck, the former Fairfax County Attorney who is acting as Trans County's legal counsel. "That we certainly hope occurs, and that is why they are being included."

According to Ruck, the council's 100 shares of Trans County stock are worth 1 percent of the company's current $100,000 net worth, but would be worth considerably more if the company is awarded one or both of the Fairfax franchises. If that happens, the council will start receiving stock dividends within five or six years, he said.

Council director Irvin Brobeck said the group's main goal in the arrangement was to ensure quality programming on cable television, but he acknowledged that the promise of stock dividends also was a significant concern. "Our second rationale was to ensure financial solvency," said Brobeck, adding that the group faces an uphill struggle annually soliciting private contributions.

The council, a private organization, is retained by the county to coordinate cultural events and evaluate grant applications from arts group and will receive $17,875 in county funds this year. The group occupies rent-free office sapce at the county's Green Springs Farm in return for maintaining an art gallery there.

Trans County's list of investors reads like a "Who's Who" of local government and business, as prominent local citizens race to link their names and influence with cable companies in hope of getting a piece of what mostthink will be a massive financial pie.

Among those in Trans County's stable are Rodney F. Page, who resigned last month as county school board chairman; Lorraine F. Foulds, a member of the Fairfax County Park Authority; Nancy Hanks, vice chairman of the Rockefeller Brother's Foundation and former chairman of the National Endowment for the Arts; Carlton C. Massey, the retired county executive for whom the main county office building is named; former Mason District supervisor Alan H. Magazine and Wolf Trap Farm Park benefactress Catherine F. Shouse.

In addition to initiating a study of the council's relationship to Trans County, the supervisors asked their staff to prepare a warning to all county boards and commissions against allying themselve with any cable TV companies until after the franchises are awarded.

The supervisors also directed preparation of a measure that would require officials of all agencies that receive county funds, to disclose their relationship with cable companies.

Supervisor Audrey Moore said the action by the board marks only the beginning of the lengthy struggle over cable television. "I can't believe all the people are involved. And you've got to believe that they've been asked because of their ability to influence a public decision," she said.