My federal tax return accepted within 48 hours. But NY state tax file has not been accepted even after a week of filing? Can you check and explain?

Correct. New York state is not accepting and processing tax returns until Monday, January 28, 2019. 

Source: NY Tax Processing

The IRS is not officially accepting tax returns until January 28, 2019 either, but they have accepted batches of test returns for processing. They will not begin to process refunds until this date. 

NY State takes a long time accepting returns.  They usually take about a week.  Have you checked the NY State website?  Last year I found out my NY return was accepted by the website before getting an email from Turbotax.  I've noticed for NY returns that I get my refund faster one year and then wait months the next year and I am filing the same number of dependents every year.  Last year I got my state refund the same date I got my federal so I expect to wait a long time this year.

I just hope NY stopped all their stupid messages.

Got an email on Friday 2/1/19 that my NY return was accepted.  I just checked the N Y State refund website and it shows that they received it.  Not bad for NY since I e-filed 1/28.  Now the waiting game begins.