A good bright red hair dye: low chemicals?

I have been dying my hair red lately, and I mean bright red, like Ariana Grande's or Ariel's(The Little Mermaid), but my mom says I can only use natural dyes(Ex. Herbatint, Naturtint). Also, I can't bleach my hair, but the red hair dye has been working fine without it.. just fine though, becuase it's not a very bright dye. Does anyone now a natural/low chemical bright red hair dye(like Ariana Grande's or The Little Mermaid's)?