What is "newform"

Etymology 1 alt. (context transitive English) To form or shape anew; reform. vb. (context transitive English) To form or shape anew; reform. Etymology 2

n. (context mathematics number theory English) A cusp form that is "new" at a given level ''N'', where the levels are the nested subgroups Γ₀(''N'') of the modular group, with ''N'' ordered by divisibility.