Possible Chern class computation error when pushing forward O(1)

I have the following code:

loadPackage "Schubert2"
B=base(5,Bundle=>(E,2,"c"))
BR=intersectionRing(B)
PSym2E=projectiveBundle(symmetricPower(2,E))
PSym2ER=intersectionRing(PSym2E)
gamma=PSym2E.StructureMap
chern(gamma_*OO_PSym2E(1))
chern(dual(symmetricPower(2,E)))
chern(symmetricPower(2,E))

Since projectiveBundle uses the classical (Fulton) convention, it should be that gamma_*OO_PSym2E(1)=dual(symmetricPower(2,E)), and thus chern(gamma_*OO_PSym2E(1))=chern(dual(symmetricPower(2,E))), but we get the following two outputs instead:

chern(gamma_*OO_PSym2E(1))=1+6*c1+(11*c1^2+4*c2)+(6*c1^3+8*c1*c2),
chern(dual(symmetricPower(2,E)))= 1-3*c1+(2*c1^2+4*c2)-4*c1*c2.

Just to double check that it wasn't just a sign convention issue, we also have

chern(symmetricPower(2,E))=1+3*c1+(2*c1^2+4*c2)+4*c1*c2.

I did the computation by hand, and I got

chern(dual(symmetricPower(2,E)))= 1-3*c1+(2*c1^2+4*c2)-4*c1*c2, 

so it seems to me that there is some issue with forming the bundle gamma_*OO_PSym2E(1).

This may be related to this issue: https://github.com/Macaulay2/M2/issues/330

Reproduce the provided Macaulay2 snippet using the Schubert2 package, focusing on projectiveBundle, StructureMap, and the pushforward of OO_PSym2E(1). Compare its Chern character with dual(symmetricPower(2,E)) and symmetricPower(2,E), then trace where the projective-bundle convention is handled. Done means the pushforward agrees with the stated Fulton convention or the discrepancy is explained and covered by a regression test.