According to the form 1041 Instructions, extracted below, if there was no income for the tax year then you do not have a filing requirement.
A trust taxable under section 641 is one with "...taxable income of estates or of any kind of property held in trust, including income received by estates of deceased persons during the period of administration or settlement of the estate..."
"The fiduciary (or one of the joint fiduciaries) must file Form 1041 for a domestic trust taxable under section 641 that has:
- Any taxable income for the tax year;
- Gross income of $600 or more (regardless of taxable income);
- A beneficiary who is a nonresident alien; or
- If you held a qualified investment in a QOF at any time during the year, you must file your return with Form 8997 attached. See the Form 8997 instructions."
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