Numerical calculation of twisted adjoint $L$-values attached to modular forms

Abstract

Doi, Hida, and Ishii have shown that the values of twisted adjoint $L$-functions $L(1,\Ad(f)\otimes\chi)$ attached to modular forms $f$ are closely connected with discriminants of Hecke fields. Goto has given a numerical example of this $L$-value for an elliptic cusp form $f$ of level $1$ and weight $20$. We shall show a method to calculate the $L$-values, which is more effective than Goto's, and give new numerical examples.