Design and performance of the upgrade of the CMS L1 trigger

During its second run of operation, the LHC delivered proton-proton collisions at a center-of-mass energy of 13 TeV with a peak instantaneous luminosity larger than $2 \times \mathrm{10^{34}\; cm^{-2}\cdot s^{-1}}$, more than double the peak luminosity reached during Run-1 and far larger than the design value. The upgraded CMS Level-1 trigger is designed to improve the performance at high luminosity and large number of simultaneous inelastic collisions per crossing (pileup). During the technical stop at the beginning of 2016, all the electronic boards of the CMS Level-1 trigger have been replaced and the upgraded electronics tested, and commissioned with data. Smarter, more sophisticated, and innovative algorithms are now the core of the first decision layer of CMS: the upgraded trigger system implements pattern recognition and MVA (Boosted Decision Tree) regression techniques in the trigger boards for $\mathrm{p_T}$ assignment, pileup subtraction, and isolation requirements for electrons and taus. In addition, the new global trigger is capable of evaluating complex selection algorithms such as those involving the invariant mass of trigger objects. The upgrade reduces the trigger rate and improves the trigger efficiency for a wide variety of physics signals. In this paper, the upgraded CMS Level-1 trigger design and its performance are described.