Why is Saturn the only large planet without any trojans? Every planet apart from Mercury and Saturn has trojans in its L4 and/or L5 points.
Mercury is easy enough to explain: It is small, has an eccentric orbit that precesses, and any trojans it has would be heavily perturbed by the Sun's gravity.
However Saturn doesn't have any of those complications. The answer given to this question is that Jupiter's gravity perturbs any trojans at Saturn's L4 and L5 points.
But if Mars, which is much less massive than Saturn and comes closer to Jupiter, can have multiple trojans then there's no reason why Saturn shouldn't.
They are pulled out of stable orbits by Jupiter.
The details are in https://ui.adsabs.harvard.edu/abs/2012jsrs.conf..225B/abstract
Full text https://syrte.obspm.fr/jsr/journees2011/pdf/baudisch.pdf

The planet Jupiter is solely responsible for the hole of instability for short time integrations
($T &lt; 10^{7}$) compared to the age of the planetary system. On the long term scale this planet also destabilizes the whole region around the Saturnian libration points. If we find in the future Trojans of Saturn,
these Trojans could only be captured asteroids, in orbits in the 1:1 MMR for a short time