method makes critical use of the Rankin-Selberg method and reduces the question of $p$-adic boundedness of the $L$-function down to that of the Fourier coefficients of the Eisenstein series that are involved in the Rankin-Selberg integral expression. For full generality, it is assumed that $p$ does not divide the level of the modular form $f$ and a crucial step is to produce another form $f_0$ such that $p$ does divide the level. Significant modifications to the method of [@Panchishkin] were required to make this work in the metaplectic case – this is Section \[pstabsection\]. Outside of this, the success of Panchishkin’s method is facilitated by the work of G. Shimura in developing the Rankin-Selberg integral expression in this setting, [@Shimuraexp], and the arithmeticity of Eisenstein series, [@Shimurabook Chapters 16–17]. Interestingly, the $p$-adic boundedness of the Eisenstein series coefficients is almost immediate in this case, making the final step of the proof simpler than that found in [@Panchishkin].

After preliminary Sections \[modformsection\] and \[Lfunsection\], we establish the $p$-stabilisation in Section \[pstabsection\]. Fairly elementary manipulations on the level of the Rankin-Selberg integral follow in Section \[tracesection\]. Sections \[thetasection\] and \[eisensteinsection\] are devoted to transformation formulae of theta series and Fourier expansions of 