A theory of local old- and newforms for representations of over a -adic field with Iwahori-invariant vectors is developed. The results are applied to Siegel modular forms of degree 2 with square-free level with respect to various congruence subgroups.
Ralf SCHMIDT. "Iwahori-spherical representations of GSp(4) and Siegel modular forms of degree 2 with square-free level." J. Math. Soc. Japan 57 (1) 259 - 293, January, 2005. https://doi.org/10.2969/jmsj/1160745825