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Leases - Supplemental Cash Flow Information (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2024	Mar. 31, 2023
Cash paid for amounts included in the measurement of lease liabilities:
Operating cash flows from operating leases	$ 18	$ 10

X

- Definition

Cash Flow, Lessee

+ References

No definition available.

+ Details

Name:	fbc_CashFlowLesseeAbstract
Namespace Prefix:	fbc_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of cash outflow from operating lease, excluding payments to bring another asset to condition and location necessary for its intended use.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 5
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479041/842-20-45-5

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-4

+ Details

Name:	us-gaap_OperatingLeasePayments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration