Indonesian prosecutors are seeking jail sentences of 18 years for an American man and 15 years for his girlfriend if they are found guilty of murdering the woman's mother while on holiday in Bali last year.
The prosecutors told the court that Tommy Schaefer and Heather Mack, who appeared in court with their two-week-old daughter, were guilty of premeditated murder.
The panel of judges could ignore the sentencing request and decide to impose the maximum, death by a firing squad, if it convicts them.
"The defendant has committed sadistic acts to her own mother," chief prosecutor Eddy Arta Wijaya told the court at Mack's trial. "However, we've decided to be lenient because she repeatedly expressed remorse and has a newborn baby."
The badly beaten body of Sheila von Wiese-Mack, 62, was found in a suitcase in the boot of a taxi outside a hotel in August.
Mr Wijaya asked the judges to declare the defendants guilty, saying that Schaefer deliberately brought a metal fruit bowl when he came to the room at the St Regis where Mack and her mother were staying, on a different floor from his own.
Mack helped stuff Schaefer's mother's body in the suitcase by sitting on it to enable her to close it, prosecutors said.
Schaefer, 21, and Mack, 19, both from Chicago, are being tried separately at the Denpasar District Court on Bali. The judges and prosecutors are the same in both trials.
The defendants sat quietly, with Schaefer on the verge of tears as the sentence request was read. The defendants and their lawyers will respond to the prosecution's case next week and verdicts are expected in late April.
Schaefer has testified that Ms von Wiese-Mack was angry with him when she learned about her daughter's pregnancy.
He said at previous court hearings that she insulted him and Mack, wanted her to have an abortion and strangled him in a heated argument before he struck her several times with the fruit bowl.
At today's hearing, another prosecutor, Ni Luh Oka Ariani Adikarini, said testimony and evidence showed that Schaefer deliberately planned to kill the victim.
"There is no excuse for the deeds of the defendant," he said and recommended the court sentence Schaefer to 18 years in jail.
The court had delayed the hearing last week because the couple's baby, Stella, became ill in prison, but doctors said the baby has recovered from jaundice.