Literally translated it should be singular, but in normal English "Mom has no brothers" sounds far better than "...brother". When using "no" to show an absence of something, the object is usually plural, even when showing the absence of one thing. eg "There are no options", "He has no coins"
@Joseph_Pate - With мой / твой , chop off the й and replace it with the ending for that case/gender/number (in this case, it would be "у моей мамы нет брата").
With наш / ваш, just add the ending directly after the ш. (у нашей мамы нет брата).
His / her / its / their (Его / её / их) do not decline at all, you just keep them there (У его мамы нет брата).