The body of Carmen Moulton, of Tyne Close Terrace in Penrith, was found at a house in the town's William Street in the early hours of Saturday.
Police said a post-mortem examination was being held to determine whether the recently banned drug was involved.
Three men aged 40, 31, and 19 and a girl aged 16 were arrested on suspicion of supplying controlled drugs.
The teenager's mother, Michelle Hodgson, said: "We are all devastated by the loss of a caring, loving daughter who was full of life and had her whole life ahead of her.
"We would appreciate being left alone to grieve and come to terms with our loss."
A Cumbria Police spokesman said: "We are investigating the circumstances surrounding the death and have informed Miss Moulton's immediate family and the local coroner.
"A post-mortem examination is expected to take place later."
The drug and its related compounds were branded Class B substances after measures were rushed through Parliament.
The Advisory Council for the Misuse of Drugs (ACMD) had recommended a ban, saying the substance was "likely to be harmful", despite incomplete research.
Mephedrone is derived from cathinone, a compound found in a plant called khat.
The laboratory-produced drug has a similar effect to amphetamines, ecstasy or cocaine.
It has been linked to a number of deaths but there has been no conclusive proof that it has been responsible for any of them on its own.