“You’re welcome to come by my office,” she tells them. “It’s just not much to see.”

This is not a politician’s false modesty. Warren’s prize for winning one of the toughest and highest profile Senate battles in the country: An office in a prefabricated building known around the Senate as “the trailer.’’

Efforts have been made to spruce up the paper-thin walls with Norman Rockwell reproductions and photographs of a Gloucester lighthouse and the Zakim Bridge. But there is no way to disguise the modest nature of the space, in a small cluster of temporary structures erected in the courtyard of a grand office building — the US Senate’s version of a mobile-home park.

Warren cracks good-natured jokes about it and insists she has far greater frustrations to confront, including complex filibuster rules that can be used by the minority to kill legislation. But her extended stay in modular housing, expected to last until June, is a freshman’s first and most tangible lesson in the plodding and idiosyncratic ways of the Senate.

In November, Warren learned from her chief of staff, Mindy Myers, that she would be confined to the equivalent of a double-wide trailer. She thought it was a joke.

But Myers, a veteran of the Senate, explained that as a freshman, Warren would have to wait for a permanent office until more senior senators decided whether they wanted an upgrade. That process, it turns out, takes months. In the meantime, freshman senators have no choice but to bide their time in temporary quarters.

To reach her office, a visitor leaves behind marble floors, vaulted ceilings, and neo-Roman columns and crosses into an environment of threadbare maroon carpeting, yellow siding, and fluorescent lights encased in drop ceilings — an atmosphere more suited to, say, used car sales than the weighty business of the nation.

Warren has a mini-fridge by her desk. Exposed fuse boxes and electrical outlets are covered by a curtain, on a wall above her couch. A room next door is crammed with cubicles and 14 staffers.

“When people come in, I say ‘Welcome to my office,’ and I give a little laugh,” Warren said. “And people give this puzzled look like ‘Huh? This isn’t quite what I envisioned.’ ”

Warren has no room for larger groups, so she meets constituents in an underground conference room in the US Capitol Visitors Center, which is about a quarter of a mile away, through a maze of tunnels.

Another new senator, Tammy Baldwin of Wisconsin, occupies the prefab structure next door to Warren, while other freshmen are housed in a variety temporary quarters, including basement committee rooms.

The House, which must move a much higher volume of representatives every two years, acts with far greater speed and efficiency. Representative Joseph P. Kennedy III of Massachusetts, for instance, and other freshmen House members moved into their new offices the day before being sworn in, after picking spaces by lottery.

The Senate’s machinations are more complex and substantial, befitting a chamber that considers itself the more deliberative body. The rules even contain obscure loopholes.

Every two years, after an election, each senator gets a 24-hour turn to inspect available offices. The order of these lengthy deliberations is based on seniority.

Even among this year’s crop of 12 freshman, Warren is rated low in seniority, because she has no previous experience in the House, in certain executive branch positions, or in governors’ mansions. That system places Warren 97th in seniority among 100 senators, her only boost coming because Massachusetts has a larger population than Nebraska and North Dakota, the home states of number 98 (Republican Deb Fischer) and number 99 (Democrat Heidi Heitkamp).

Paradoxically, number 100 on the list, Massachusetts Democrat William “Mo’’ Cowan — the interim senator appointed to fill the seat vacated by Secretary of State John F. Kerry — currently occupies a nicely appointed suite that previously belonged to Republican Scott Brown, whom Warren defeated.

Cowan benefits from a rule that permits replacement appointees to squat in a vacant office before taking over the departed senator’s old space. In his case, he will get Kerry’s office, which is even nicer than Brown’s, once it is emptied of Kerry’s collection of art and memorabilia and repainted.