We demonstrate the coupling of multipolar surface plasmons with photonic modes in periodic arrays of metallic nanoantennas. This coupling leads to sharp resonances known as lattice surface modes. In spite of the weak interaction of multipolar surface plasmons with light, lattice surface modes provide an efficient radiative decay channel for emitters in the proximity of the array. We observe a tenfold emission enhancement of dyes coupled to lattice resonances. Lattice surface modes light up multipolar plasmonic resonances, opening new possibilities for fluorescence spectroscopies.