Correction and addendum to: The Fourier expansion of Hecke operators for vector-valued modular forms

TL;DR

This paper corrects errors in previous formulas related to Hecke operators for vector-valued modular forms and provides a new formula connecting different Hecke operators, clarifying their relationships.

Contribution

It rectifies inaccuracies in earlier work and introduces a new formula linking various Hecke operators for vector-valued modular forms.

Findings

Corrected formulas in Theorems 5.2 and 5.4 of previous work

Derived a new relation between Hecke operators using a formula from extcite{BCJ}

Clarified the structure of Hecke operators for vector-valued modular forms

Abstract

We correct a mistake in \cite{St} leading to erroneous formulas in Theorems 5.2 and 5.4. As an immediate corollary of a formula in \cite{BCJ} we give a formula, which relates the Hecke operators $T(p^2)\circ T(p^{2l-2})$, $T(p^{2l})$ and $T(p^{2l-4})$ and comment on it.