Description of Plan - Narrative (Details) - EBP 004	12 Months Ended
Dec. 31, 2025 USD ($)
EBP, Description of Plan [Line Items]
Employer contribution vesting amount	$ 0
Administrative fee	39
Forfeited nonvested account, decrease from employer contribution	331,209
Nonvested amount	545,099
Forfeited nonvested account	1,417
Note receivable from participant, account, maximum borrowing, amount	$ 50,000
Note receivable from participant, account, maximum borrowing, to total account, percentage	50.00%
General loan, borrowing term	5 years
Primary residence, borrowing term	30 years
Investment, maturity date	30 years
Dividends paid to participants	$ 62,393
EBP, Safe Harbor Matching Contribution, Tranche One
EBP, Description of Plan [Line Items]
Participant compensation matched, percentage	3.00%
Matching percentage	100.00%
EBP, Employer Safe Harbor Matching Conributions, Tranche Two
EBP, Description of Plan [Line Items]
Participant compensation matched, percentage	2.00%
Matching percentage	50.00%
Minimum
EBP, Description of Plan [Line Items]
Annual fixed rate contribution, percentage	1.00%
Asset held for investment, participant loan, interest rate	2.25%
Maximum
EBP, Description of Plan [Line Items]
Annual fixed rate contribution, percentage	60.00%
Participant compensation matched, percentage	5.00%
Asset held for investment, participant loan, interest rate	9.50%

EBP, Asset Held for Investment, Participant Loan, Maturity Period

No definition available.

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- Definition

EBP, Dividends Paid To Participants

+ References

No definition available.

+ Details

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Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

EBP, Employer Contribution, Discretionary Employer Contribution

+ References

No definition available.

+ Details

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Namespace Prefix:	fbc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

EBP, Employer Contribution, Nonvested Amount

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

EBP, Note Receivable From Participant, Account, Primary Residence, Maximum Borrowing Term

+ References

No definition available.

+ Details

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- Definition

EBP, Note Receivable From Participant, General Loan, Maximum Borrowing Term

+ References

No definition available.

+ Details

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- Definition

EBP, Participant Accounts, Administrative Fee

+ References

No definition available.

+ Details

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

- Definition

EBP, Participant Contribution, Contribution to Eligible Compensation, Percentage

+ References

No definition available.

+ Details

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Namespace Prefix:	fbc_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478416/962-205-50-1

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of employer matching contribution on eligible participant contribution to employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of participant compensation eligible for employer matching contribution for participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of plan asset, in forfeited nonvested account, no longer allocated to participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of decrease in forfeited nonvested account of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) from employer contribution.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 962
-SubTopic 325
-Name Accounting Standards Codification
-Section 55
-Paragraph 17
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478873/962-325-55-17

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (j)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478416/962-205-50-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-04(5)(c))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of maximum account balance that participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) can borrow.

+ References

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Percentage of maximum account balance that participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) can borrow to total participant account balance.

+ References

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
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Period Type:	instant

- Definition

Interest rate on participant loan in schedule of asset held for investment of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Name Employee Retirement Income Security Act of 1974
-Number 2520
-Section 103
-Subsection 10
-Paragraph b
-Subparagraph (1)(i)(D)
-Publisher DOL-EBSA

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-05(a)(Schedule I))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

+ Details

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Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Details

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Namespace Prefix:
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- Details

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- Details

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- Details

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