---
title: "Dimensions of Spaces"
canonical: "https://docs.magma-maths.org/ModularArithmeticGeometry/BrandtModules/ModBrdt-dimension-formulas.html"
source: "https://docs.magma-maths.org/ModularArithmeticGeometry/BrandtModules/ModBrdt-dimension-formulas.md"
part: "Modular Arithmetic Geometry"
chapter: "Brandt Modules"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Modular Arithmetic Geometry", "source": "../index-modular-arithmetic-geometry.md"}
  - {"title": "Brandt Modules", "source": "index-brandt-modules.md"}
prev: {"title": "$q$-Expansions", "source": "qexpansions.md"}
next: {"title": "Brandt Modules Over $F_q[t]$", "source": "ModBrdt-fldfunrat.md"}
intrinsics:
  - {"name": "BrandtModuleDimension", "signature": "BrandtModuleDimension(D, N): RngIntElt, RngIntElt -> RngIntElt"}
examples:
  - "ex-4ee604"
---

# Dimensions of Spaces

<a id="function-brandtmoduledimension-rngintelt-rngintelt"></a>
## `BrandtModuleDimension(D, N): RngIntElt, RngIntElt -> RngIntElt`

The dimension of the Brandt module of level $(D,N)$, computed by means of standard formulas.

<a id="example-ex-4ee604"></a>
## `Example: Dimensions of Brandt Modules (ex-4ee604)`

In the following example we demonstrate the computation of the dimensions of the Brandt modules for the sequence of Eichler orders of index $3^i$ in a maximal order in the quaternion algebra of discriminant $2\cdot 3 \cdot 7$.

```magma
> D := 2*5*7;
> for i in [0..10] do
>     BrandtModuleDimension(D,3^i);
> end for;
2
8
24
72
216
648
1944
5832
17496
52488
157464
```