What is the test for remand in a criminal case where a defendant's sentence was based on an incorrect assessment of his criminal record?

Further, "[d]efendants are entitled to sentencing decisions made in the exercise of the 'informed discretion' of the sentencing court. [Citations.] A court which is unaware of the scope of its discretionary powers can no more exercise that 'informed discretion' than one whose sentence is or may have been based on misinformation regarding a material aspect of a defendant's record." (People v. Belmontes (1983) 34 Cal.3d. 335, 348, fn. 8.) "Generally, when the record shows that the trial court proceeded with sentencing on the erroneous assumption it lacked discretion, remand is necessary so that the trial court may have the opportunity to exercise its sentencing discretion at a new sentencing hearing." (People v. Brown (2007) 147 Cal.App.4th 1213, 1228.)