Iwasawa invariants of Bertolini--Darmon Theta Elements

In this article we study the Iwasawa invariants of Bertolini–Darmon theta elements in the anticyclotomic ${\mathbb{Z}}_p$-extension of an imaginary quadratic field $K$ for weight two modular forms $f\in S_2({\mathrm{\Gamma }}_0(N))$. We cover both the cases of ordinary and non-ordinary reduction at a prime $p$. Our results extend the known results of Pollack–Weston and Leonard–Lei in the cyclotomic setting.