Abstract
Let $f$ be a cuspidal $CM$ modular form of weight $1$ and level $N$ which is irregular at $p$.The primary goal of this thesis is to investigate the behavior $L_b-$ideal at $f$ without knowing the modules of overconvergent modular symbols $M^+$ and $M^-$. These modules are $T-$modules which are free of finite rank $n$ over $R$. We present a full classification such modules for $n=2$ and $3$ and partial classification for $n=4$. We also establish that the $L_b-$ideal is not principal for $n\ne 2$ which means that there is no single $p-$adic adjoint $L-$function near $f$.