Two new polls show Elizabeth Warren leading Senator Scott Brown, one by six points and the other by two points, suggesting a possible bump for the Democratic candidate following the two parties’ conventions.

A Springfield Republican poll, taken Sept. 6 through Sept. 13 by the Western New England University Polling Institute, shows Warren leading Brown, a Republican, 50 percent to 44 percent among likely voters. The group polled 444 likely voters and reported a margin of error of plus or minus 4.6 percent. (The newspaper reported a wider margin of support for Warren, 12 percent, among a slightly larger group of registered voters polled.)

Polling began the same day the Democratic convention was concluding, according to the newspaper, a day after Warren delivered a nationally televised speech to delegates in Charlotte. The last time the newspaper polled, in late May, Warren led by two points, 45 percent to 43 percent.

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The other poll, taken Sept. 13 through Sept. 16 by Public Policy Polling, a Democratic-leaning group, shows Warren leading Brown 48 percent to 46 percent among likely voters. The group polled 876 likely voters and reported a margin of error of plus or minus 3.3 percent.

An August poll taken by Public Policy Polling showed Brown ahead by 5 points, 49 percent to 44 percent.

The fluctuations among the various polls support the expectation in both campaigns that the race will remain close until Election Day.

The first of four televised debates is scheduled for Thursday night, and is expected to add a new dimension to the campaign.