Can parents read my texts online

[Nexus4]

Hello, my parents recently threatened to have my texts printed out. They said they could have them printed out or they could just go online and read them all. I don't want my conversation with my girlfriend to be seen by them. They aren't very tech savvy at all. I believe that this is just a threat, but I need an experts response to this. My mother is the account owner of both mine and her phone. I have a Nexus 4 obviously using Teuls.

Thanks.

[Nighthawk · Accepted solution]

Can't read texts online though the Telus account. Now there are Android apps that would allow them to monitor any text message that is sent/ received but they would need access to your phone to install them.