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Leases - Supplemental Cash Flow Information (Details) - USD ($) $ in Millions | 3 Months Ended | 6 Months Ended
--- | --- | ---
Jun. 30, 2024 | Jun. 30, 2023 | Jun. 30, 2024 | Jun. 30, 2023
Cash paid for amounts included in the measurement of lease liabilities: |  |  |  |
Operating cash flows from operating leases | $ 18 | $ 20 | $ 36 | $ 30

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- 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

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- 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