@dublove you are changing your question everytime. First you said you want to open Character Style panel, in the post heading you said Style options. Now you are saying New Character Style dialog. Be sure what you want. I am listing all options below
Open Character Style Panel
app.panels.itemByName("Character Styles").visible = true
Open Style Options of Character Style Panel. For this to work a style should be selected on the panel
app.scriptMenuActions.itemByID(8453).invoke();
To open new character style dialog
app.scriptMenuActions.itemByID(8462).invoke();
Regarding the ID’s i am not sure they are available as some documentation. You need to traverse the menuActions to get them