Thank you for your question.
In order to know this, you have to figure the federal tax return. We can not figure your actual tax, because not only do we not have a federal form 706, but we also do not know what the itemized items are in the federal estate. While you say the estate is valued at 1.24 million, for tax purposes it may not be.
According to my estimate, because of the gift exclusions, and federal exemptions, there will most definately be no federal estate tax due.
Given the information on hand, I can give you a not more than figure for estate tax.
NY only taxes the amount that exceeds federal estate by 1,000,000 dollars.
So you would not pay estate taxes, if any at all, on more than 240,000. The estate tax rate is 16%. So you can expect to pay no more than 36,400 dollars in estate taxes to NY state.
NOTE: The persons who receive the inheritance do not pay the estate tax. The estate taxes are paid out of the estate BEFORE the estate is distributed to the beneficiaries. The executor is responsible for making that happen.