bandmates, family and friends gathered to lay her to rest Tuesday in the band's hometown.
The surviving Cranberries -- Noel Hogan, Mike Hogan and Fergal Lawler -- were in Limerick for her funeral service at St. Ailbe's Church ... the church where she once played and sang in the choir.
Her loved ones, as well as hundreds of fans, have been mourning for several days ... beginning with a memorial service on Sunday.
Doloroes was found dead in a London hotel room last week. As for cause of death ... her reps and police will only say she died suddenly. She was 46.