BOSTON — A federal judge has ordered the longtime girlfriend of former Boston crime boss James “Whitey” Bulger to remain in custody without bail while she awaits trial on charges stemming from allegations that she helped him evade capture for 16 years.

U.S. Magistrate Judge Jennifer Boal today accepted Catherine Greig’s voluntary offer to remain in custody while reserving the right to seek bail later.

Bulger and Greig were arrested last month in Santa Monica, Calif. Bulger is charged with participating in 19 murders. Greig is charged with harboring a fugitive.

Bulger has pleaded not guilty.

During a bail hearing Wednesday, Greig’s attorney said she would voluntarily remain locked up while he gathers more information to support his request that she be granted bail and placed on an electronic monitoring system.