The Roth IRA contribution limit is independent of defined contribution plan limits. However, defined contribution plans can offer a "designated Roth account" (which is not a Roth IRA) that is subject to the limits for defined contribution plans.
The amount of your compensation and the terms of the defined contribution plan will determine if you are able to contribute a total of $57,000 to the defined contribution plan and separately $6,000 to a Roth IRA. Deductible contributions to the defined contribution plan (including elective deferrals to the traditional account in the plan but not elective contributions to a designated Roth account in the plan) reduce the amount of compensation available to contribute to a Roth IRA. Your eligibility to contribute to a Roth IRA also depends on your filing status and modified AGI for the purpose, and someone with sufficient income to contribute $57,000 to a defined contribution plan is likely to have a modified AGI that exceeds the limit above which one is not eligible to contribute to a Roth IRA.
