One after another last week, some of the most powerful names in the Senate came forward with their requests -- an extra room for Jesse Helms, more telephones for Ted Kennedy.

And there, deliberating on their fates, was Sen. Charles McC. Mathias (R-Md.), for the first time in a quarter-century of elective politics a power-wielding member of the marjority party.

Mathias is chairman of the Senate Committee on Rules and Administration. It may not be Appropriations or Foreign Relations or one of the other major committees that chart the course of the nation, but it was the only chairmanship available to him when the Republicans took control of the Senate for the 97th Congress.

His committee has limited authority -- its jurisdiction includes election laws and presidential succession -- but it is in its role as landlord of the Senate, dispensing office space and parking slots, that it derives its power. Mathias is making the most of it.

In a world where location of offices and number of employes are the indices of prestige, Mathias is the imperial landlord and employment agent. He began exercising his clout by promoting several of his longtime aides, hiring additional loyal supporters and awarding expanded quarters to his personal staff.

Having taken care of his own needs, he has now, in the finest tradition of power brokers, set about trimming request of his colleagues and ruefully deploring "the $1 billion Congress."

Sitting in a swivel chair in one of the most ornate rooms on Capitol Hill, behind a nameplate that identifies him as "chairman," Mathias can accomplish by fiat what before he had to try to do with persuasion, logic or intelligence alone.

Mathias of the Majority is a politician with a broader view. He swapped a subcommittee that could have directed pork barrel projects to Baltimore and the Chesapeake Bay for one that deals with the defense of Europe, and in doing, gave up breakfasts with constituents for early morning tutoring in French.

Today, in compliance with a law signed by President Carter in December and endorsed by the new Republican Senate leadership, Mathias's committee will attempt to reduce the Senate's operating budget by 10 percent. Mathias has already cut his own committee's expenses, but now he must eliminate $300,000 or so from the budgets of committees headed by some of the most powerful, stubborn and hardball playing politicians in the nation.

If last week's three days of hearings is an indication, Mathias will attempt to reach the decision by consensus. He showed little inclination to club his colleagues into submission.

"There is no need to brandish it [power]," the senior senator from Maryland, newly re-elected to a third term, said during a break in the hearings.

The suppliants who came before him last week were a procession of odd couples -- Hatch and Kennedy, Helms and Huddleston, Dole and Long - made stranger by the shift in power resulting from last November's election that made Mathias and other Republicans the majority party in the Senate for the first time since 1954.

Mathias and the ranking minority member of the Rules Committee, Sen. Wendell H. Ford (D-Ky.) played the good cop-bad cop routine, with Mathias suggesting and cajoling and Ford barking and badgering, attempting to get their Senate colleagues to perform the unnatural political act of cutting their own budgets.

When Mathias suggested that the $40,000 request for telephone service for the Labor Committee was "an anomoly," Sen. Edward M. Kennedy (D-Mass.), the erstwhile presidential candidate, was reduced to defending long distance telephone calls by a committee chaired by Orrin Hatch, the Utah conservative.

"Mr. Chairman," said Kennedy, "the minority agrees [with Hatch] that this is a bare bones budget." The large telephone charge is a result of Labor being "one of the most active committees," Kennedy said deferentially.

Sen. Ernest F. Hollings (D-S.C.), told Mathias that as ranking minority member of the Budget Committee he was "prepared to be reprimanded." He said that although he was reelected with 73 percent of the vote, he returned to Washington "and had to fire 20 staffers. I feel like I won a sweepstakes but got paid in Confederate-money."

Mathias told Hollings, "you sound like a country lawyer who needs an evil partner to do the dirty work. "We are prepared to be your devil partner."

The Judiciary Committee, as the result of its dubious distinction of having the largest budget ($5.9 million) and most employes (192) in the Senate, was a frequent object of finger-pointing.

Hollings said it was "very easy" for its new chairman, fellow South Carolinian Strom Thurmond, to reduce his budget "because the committee previously had a distinguished chairman (Kennedy) who used it for personal projects."

Thurmond proposes to get along with 58 fewer employes, and $1.6 million less money this year, but even that did not satisfy Mathias and Ford, who attempted to persuade Thurmond to give up some of the 66 rooms that the committee occupies.

"Why, you'll have fewer than three people to a room," said Ford in mock amazement. "Sir," replied Thurmond slyly, "they're mightly small rooms."

Tempers flared during the presentation by Finance Committee Chairman Robert J. Dole of Kansas and ranking minority spokesman Long. Ford harped about their refusal to cut anything, even though the committee had a surplus from last year of $553,066, more than one-fourth of its budget.

"I just wish you had found the kind of cuts that Judiciary had," growled Ford.

"By my standards, son," snapped Ford's Democratic colleague Long, "Judiciary could have been reduced by 75 percent."

To Long, Mathias invoked the words of a former Rules Committee chairman, the late Harry Flood Byrd, who was fond of saying that the budget request "may be a lean lamb, but it hasn't been fleeced yet."

Ford assured Dole, who let Long do most of the talking, that "you are not going to be [the only] lamb led to slaughter. Other will bleed a little, too."

Of the Finance Committee's $21,000 request for periodicals, Mathias observed, "your staffers obviously are avid readers. They ought to be well informed."

When discussing the Banking Committee, Ford complained to Sen. Jake Garn (R-Utah) that Democrats were not getting their fair share of staffers in the shift of power from this party to the GOP. Mathias, employing the prerogative of the chair, got the last word on that discussion: "The minority is being treated better than in the past," Mathias said with the authority of one who has been there. "At one time, the minority share was zero."