Namespace ModularFormClass 14 theorems
- Tₚ f is bounded at every cusp
ModularFormClass.isBoundedAt_heckeT0 below · cited by 0 · depth 8 - A modular form is determined by its q-expansion
ModularFormClass.eq_of_forall_qCoeff_eq0 below · cited by 39 · depth 9 - q-expansion coefficients of Tₚ f
ModularFormClass.qCoeff_heckeT0 below · cited by 35 · depth 9 - q-coefficients of Uₚ: aₙ(Uₚf)=aₙₚ(f)
ModularFormClass.qCoeff_heckeU0 below · cited by 59 · depth 9 - Tₚ f = c f tested on q-expansion coefficients
ModularFormClass.heckeT_eq_smul_iff5 below · cited by 2 · depth 10 - Commutation of Tₚ and U_q for coprime p,q
ModularFormClass.heckeT_heckeU_comm10 below · cited by 4 · depth 10 - Uₚ f = c f iff aₙₚ = c aₙ for all n
ModularFormClass.heckeU_eq_smul_iff5 below · cited by 2 · depth 10 - q-expansion of f(dτ): coefficients shift by d
ModularFormClass.qCoeff_comp_heckeDiagMatrix_smul0 below · cited by 58 · depth 10 - Hecke translates Tₚ, T_q commute for coprime p,q
ModularFormClass.heckeT_heckeT_comm6 below · cited by 2 · depth 11 - Commutativity of the Hecke operators Uₚ and U_q
ModularFormClass.heckeU_heckeU_comm6 below · cited by 1 · depth 11 - q-expansion of Tₚ f is Uₚ + p^{k-1}Vₚ applied to that of f
ModularFormClass.qExpansion_heckeT_eq_heckeT1 below · cited by 1 · depth 11 - q-expansion of Uₚf equals formal Uₚ of the q-expansion
ModularFormClass.qExpansion_heckeU_eq_heckeU1 below · cited by 10 · depth 12 - Slashing a modular form by a rational matrix preserves cusp boundedness
ModularFormClass.isBoundedAt_slash_ratCast0 below · cited by 1 · depth 19 - Uₚ f is bounded at every cusp
ModularFormClass.isBoundedAt_heckeU0 below · cited by 2 · depth 26