From AIM, Section 5-4-1:

2. Pilots navigating on STAR/RNAV STAR/FMSP procedures shall maintain last assigned altitude until receiving authorization to descend so as to comply with all published/issued restrictions. This authorization will contain the phraseology “DESCEND VIA.”

(a) Clearance to “descend via” authorizes pilots to:

(1) Vertically and laterally navigate on a STAR/RNAV STAR/FMSP.

(2) When cleared to a waypoint depicted on a STAR/RNAV STAR/FMSP, to descend from a previously assigned altitude at pilot's discretion to the altitude depicted for that waypoint, and once established on the depicted arrival, to navigate laterally and vertically to meet all published restrictions.

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Of course, the above mentioned notam clarifies the procedure for this particular airfield. This AIM reference is given as reference for most situations.