Returns true if and only if M is an ambient space. Ambient spaces are those space constructed in Section Ambient Spaces.
Returns true if M is contained in the cuspidal subspace of the ambient space.
Returns true if M is contained in the Eisenstein subspace of the ambient space.
Returns true if f is an Eisenstein newform or was computed using the intrinsic EisensteinSeries. (See Section Eisenstein Series.)
Returns true if M is a space of modular forms for Γ0(N).
Returns true if M was created explicitly as a space of modular forms for Γ1(N), or if the AmbientSpace of M is such a space. (Note that IsGamma1 will return false for any space ModularForms(chars,k), even if chars consists of all mod N Dirichlet characters.)
Returns true if M is contained in the new subspace of its AmbientSpace.
Returns true if f was created using Newforms. (Sometimes true in other cases in which f is obviously a newform. In number theory, "newform" means "normalized eigenform that lies in the new subspace".)
Returns true if and only if M is the ring of all modular forms over a given ring.
> M := ModularForms(Gamma1(11),3); > f := Newform(M,1); > IsAmbientSpace(M); true > IsAmbientSpace(CuspidalSubspace(M)); false > IsCuspidal(M); false > IsCuspidal(CuspidalSubspace(M)); true > IsEisenstein(CuspidalSubspace(M)); false > IsEisenstein(EisensteinSubspace(M)); true > IsGamma1(M); true > IsNew(M); true > IsNewform(M.1); false > IsNewform(f); true > IsRingOfAllModularForms(M); false > Level(f); 11 > Level(M); 11 > Weight(f); 3 > Weight(M); 3 > Weight(M.1); 3