The programme, starring Josh Hartnett and Eva Green, was recognised in categories including costume, make-up and hair, and production design.
BBC Two drama The Honourable Woman and BBC Three documentary Life & Death Row both landed four nods.
The awards will be handed out at a ceremony on 26 April.
Other shows which were nominated in multiple categories include Strictly Come Dancing, BBC Two's Peaky Blinders and fantasy drama Da Vinci's Demons, which received three nods each.
Ripper Street, which was originally broadcast on BBC One, but revived on Amazon's Prime Instant Video, also scored two nominations - the first Bafta recognition for a programme shown on the subscription service.
The comedy writer category features a number of well-known writer-performers.
James Corden and Mathew Baynton are nominated for a second consecutive year for The Wrong Mans, while Reece Shearsmith and Steve Pemberton are up for dark comedy Inside No.9.
They go up against Arthur Matthews and Matt Berry for Toast of London and Mackenzie Crook for Detectorists.
Among the other programmes nominated across the 20 categories include Doctor Who, Ant & Dec's Saturday Night Takeaway, The Apprentice, Line of Duty, Downton Abbey and The X Factor.
Industry-renowned vision mixer Hilary Briegel will receive this year's Bafta Special Award, recognising her extensive work on productions including Absolutely Fabulous, Only Fools and Horses, Newsnight and the Olympic Games.
The full list of nominations are on the Bafta website.
Actor Stephen Mangan will return to host this year's ceremony, held at The Brewery in London.
Sky's horror series Penny Dreadful has scored five nominations at this year's Bafta Craft Awards, which honour television's behind-the-scenes talent.