I would like to jump to the next (or prev) line, always a multiple of
"tline".

let tline = 16

This calculates how many more lines to jump
useful with "j"

:echo tline - line(".") % tline

This calculates the line to jump to
useful with "G"

:echo ( line(".") / tline + 1 ) * tline

How to create a mapping?

This does NOT work.

:nmap J execute "normal " . tline - line('.') % tline . "j"

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