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Fix a prime $p$ and a cuspidal newform $f$ of level coprime to $p$ with$a_p=0$. Attached to $f$ are signed $p$-adic $L$-functions $L_p^\pm(f)$ andMazur-Tate elements $\theta_n(f)$, both of which encode arithmetic data about$f$ along the cyclotomic $\mathbf{Z}_p$-extension of $\mathbf{Q}$. We computethe Iwasawa invariants of Mazur-Tate elements in terms of the correspondinginvariants of the signed $p$-adic $L$-functions. As corollaries, we determinethe $p$-adic valuation of critical values of the $L$-function of $f$, anddescribe a relation between the Iwasawa invariants of congruent modular formsof weights 2 and $p+1$. Our results provide an asymptotic method for computingthe signed Iwasawa invariants attached to newforms of any weight $k\geq 2$ with$a_p=0$.

Iwasawa invariants of modular forms with $a_p=0$