The baby is in a stable condition at the Children's Hospital at Westmead, after his rescue on Sunday. His cries were heard by passers-by on the side of the M7.

The woman is believed to have pushed him down the drain, where he fell 2.4 metres, one day after giving birth at Blacktown Hospital. She has been charged with attempted murder.

The boy survived for six days down the drain before a man cycling with his daughter recognised the cries coming from the drain as those of a newborn baby and called police to help rescue the boy.

Police say it is unclear how the baby survived for so long, apparently without food or water, after he was dumped in the drain on Tuesday last week.

Checks of recent hospital births and doorknocking of the area led police to the mother on Sunday afternoon. She was arrested after attending Blacktown police station about 2pm on Sunday.

The baby's name cannot be published for legal reasons but News Limited is reporting that the woman reportedly chose a biblical name.

She has no criminal history and has been living with her aunt, uncle and cousin in an apartment in Quakers Hill.

She admitted to police that she dumped the boy down the drain knowing it would kill him, court papers show.

The case against her was heard briefly in Blacktown Local Court on Monday.

Documents before the court allege that, when interviewed by police, the woman "made full admissions to putting the less than 24 hour old baby down a 2.4 metre drain knowing it may kill the baby".

She did not appear in court and did not apply for bail.

Her family were in court to hear proceedings and, as they left the courthouse, were abused by angry members of the public, who yelled: "You ought to be ashamed."

Documents before the court court revealed police had opposed her bail as they viewed her as a flight risk as her parents and siblings live in Samoa.

Magistrate Tim Keady ordered the woman be medically assessed while in custody.

The matter was adjourned to Penrith Local Court on Friday.

Fairfax Media