Non-exempt Transactions (Details) - USD ($)	12 Months Ended
Dec. 31, 2025	Dec. 31, 2024
EBP 004
EBP, Non-Exempt Transactions [Line Items]
Employee withholding taxes, amount not remitted	$ 0	$ 4,778

EBP, Employee Withholding Taxes, Amount Not Remitted

No definition available.

Name:	fbc_EBPEmployeeWithholdingTaxesAmountNotRemitted
Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration