Theorems · Theorem · number theory
ModularForm.directSum_of_pow
∀ {Γ : Subgroup (GL (Fin 2) ℝ)} [inst : Γ.HasDetPlusMinusOne] {k : ℤ} (f : ModularForm Γ k) (n : ℕ),
(DirectSum.of (ModularForm Γ) k) f ^ n = (DirectSum.of (ModularForm Γ) (↑n * k)) (f.pow n)The n-th power of DirectSum.of _ k f lands in grade n * k and is given by f.pow n.
- Defined in
- Mathlib.NumberTheory.ModularForms.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Subgroup.HasDetPlusMinusOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Matrixstatement · cited by 4,303
- Subgroupstatement and proof · cited by 3,593
- AddMonoidHomstatement · cited by 3,230
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- DirectSumstatement · cited by 446
- DirectSum.ofstatement · cited by 122
- ModularFormstatement and proof · cited by 98
- Subgroup.HasDetPlusMinusOnestatement and proof · cited by 57
- ModularForm.powstatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- ModularForm.discriminant_eq_E₄_cube_sub_E₆_sq_gradedproof · cited by 0