Sooner or later your mom is bound to find out you have been dating someone and it will only complicate the situation further. Most likely she will be angry and it is bound to damage the trust in your relationship. It would be a good idea to get more information from your mother on why she thinks you are not “emotionally mature enough” to date. Many parents feel that 13 years old is too young to date and it has nothing to do with their own personal relationship history. Dating and relationships can be very complicated because they can involve many intense emotions. Also at your age teenagers tend to feel a lot of social pressure to be in a relationship as a way of validating their self esteem. Because of this pressure some young people can be put in situations where they are uncomfortable or could get hurt.
Talking to your mom may not give you the outcome you desire but it will show that you are taking the issue seriously and that is part of being mature. Perhaps you could compromise and propose “group dating.” Many parents are more comfortable with this type of situation because they feel the situation is safer.
TeenHealthFX is concerned that you did not mention the age of your boyfriend. When someone in the relationship is much older, there tends to be a "power differential" which means that there is a greater potential for you to be exploited. Also research has shown that girls who date someone older then themselves there is a tendency to have sex before they want to, have higher pregnancy rates and higher rates of STDs.