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(e) Limitations where credit is claimed under this section for income taxes paid to both a state and also to one or more of its political subdivisions. Where both a state and one or more of its political subdivisions impose income taxes on the same or different amounts of a resident taxpayer's ordinary income portion (or part thereof) of a lump sum distribution derived from sources within such state and political subdivision (which income is also subject to the separate tax under section 603 of the Tax Law), the maximum credit allowable is the lowest of the amounts determined after computing the following three limitations:
(1) The credit cannot exceed the total of the income taxes payable by such taxpayer to the other state and the other political subdivision or subdivisions on the ordinary income portion (or part thereof) of a lump sum distribution (determined separately for the other state and its subdivision [s] in accordance with the provisions of paragraph [b][1] and/or [2] of this section and then combined). For notification of a change of income tax payable to the other state or a subdivision thereof, see paragraph (d)(1) of this section.
(2) The credit cannot exceed the amount obtained by multiplying the New York State separate tax payable by the taxpayer on the ordinary income portion (or part thereof) of a lump sum distribution by the percentage determined by dividing the taxpayer's portion (or part thereof) of such income subject to taxation by such other jurisdiction (the numerator) by the taxpayer's portion (or part thereof) of such income subject to the New York State separate tax imposed thereon by section 603 of the Tax Law (the denominator). Where different amounts of the ordinary income portion (or part thereof) are subject to taxation by both the other state and by one or more of its subdivisions, the larger amount of such income subject to tax by either the state or one or more of its subdivisions must be used in the numerator of this computation.
(3) The credit for the total income taxes paid by the taxpayer to both another state and one or more of its political subdivisions on the ordinary income portion (or part thereof) of a lump sum distribution cannot reduce the New York State separate tax payable under section 603 of the Tax Law to an amount less than would have been due under such section if the ordinary income portion (or part thereof) of the lump sum distribution subject to taxation by the other jurisdictions (or where different amounts of such income are subject to taxation by the other jurisdictions, the larger of such amounts) were excluded from the ordinary income portion (or part thereof) of the lump sum distribution reported in accordance with section 603 of the Tax Law.