Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors

Century Bancorp, Inc.:

We consent to the incorporation by reference in the registration statements (Nos. 333-118208, 333-58196, and 333-29987) on Form S-8 of Century Bancorp, Inc. of our reports dated March 13, 2020, with respect to the consolidated balance sheets of Century Bancorp, Inc. and its subsidiary as of December 31, 2019 and 2018, the related consolidated statements of income, comprehensive income, changes in stockholders’ equity, and cash flows for each of the years in the three-year period ended December 31, 2019, and the related notes (collectively, the consolidated financial statements), and the effectiveness of internal control over financial reporting as of December 31, 2019, which reports appear in the December 31, 2019 annual report on Form 10-K of Century Bancorp, Inc.

/s/ KPMG LLP

Boston, Massachusetts

March 13, 2020