The Quotient $L(A,1)/\Omega _{A}$

Fix a newform $f\in S_2(\Gamma_0(N))$, let $I_f$ be the annihilator of $f$ in $\mathbf{T}$, and $A=A_f=J_0(N)/I_f J_0(N)$ the corresponding optimal quotient. Suppose for the rest of this section that $L(A,1)\neq 0$.