In general, it is difficult to determine the dimension of the space of Siegel modular forms with low weight. In this paper, we consider the spaces of modular forms belonging to the principal congruence subgroup of level 3 as the representation spaces of the finite symplectic group to calculate their dimensions.
"On the graded ring of Siegel modular forms of degree 2, level 3." J. Math. Soc. Japan 56 (2) 375 - 403, April, 2004. https://doi.org/10.2969/jmsj/1191418636