Theorems · Theorem · number theory

ModularForm.sub_smul_isCuspForm

∀ {k : ℤ} (f g : ModularForm (Matrix.SpecialLinearGroup.mapGL ℝ).range k),
  (PowerSeries.coeff 0) (UpperHalfPlane.qExpansion 1 ⇑g) = 1 →
    (f - (PowerSeries.coeff 0) (UpperHalfPlane.qExpansion 1 ⇑f) • g).IsCuspForm

Subtracting (qExpansion 1 f).coeff 0 • g from f (where g has constant qExpansion 1) gives a cusp form.

Defined in: Mathlib.NumberTheory.ModularForms.CuspFormSubmodule
Cited by: 0 results in Mathlib
Foundations: Depth 296 from the axioms · uses propext, Classical.choice, Quot.sound

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