Let Sk​(Γpara(N)) be the space of Siegel paramodular forms
of level N and weight k. Let p∤N and let χ be a nontrivial
quadratic Dirichlet character mod p. Based on our previous work, we define a
linear twisting map Tχ​:Sk​(Γpara(N))→Sk​(Γpara(Np4)). We calculate an explicit expression for
this twist and give the commutation relations of this map with the Hecke
operators and Atkin-Lehner involution for primes â„“î€ =p.Comment: 64 pages. In version 2, the paper has been shortened significantly
and lengthy, technical proofs given in a separate appendix. In version 3, two
typos are corrected. In version 4, we have included the full details of the
proof of the local twisting theorem in the paper and improved the results
with the L-function theore