# Creation of Admissible Representations

One starts with a classical cuspidal eigenform, given as a space of modular symbols.

## `LocalComponent(M, p): ModSym, RngIntElt -> RepLoc`

This returns the admissible representation of ${\operatorname{GL}}({\mathbb{Q}}_p)$ associated to the cuspidal eigenform specified by $M$. Here $M$ must be a space of modular symbols that is cuspidal and contains only a single Galois conjugacy class of newforms. (Such spaces are created using `NewformDecomposition`).

## `Example: Creation Example (ex-7bb24b)`

We create the local component at $11$ of the representation associated to the newform of level $11$ and weight $2$. We specify the newform as a space of modular symbols of level $11$, weight $2$ and sign $+1.$

```magma
> S11 := CuspidalSubspace(ModularSymbols(11, 2, 1));
> newform_spaces := NewformDecomposition(S11);
> newform_spaces;
[
Modular symbols space for Gamma_0(11) of weight 2 and dimension 1
   over Rational Field
]
> Eigenform(newform_spaces[1]);
q - 2*q^2 - q^3 + 2*q^4 + q^5 + 2*q^6 - 2*q^7 + O(q^8)
> LocalComponent(newform_spaces[1], 11);
Steinberg Representation of GL(2,Q_11)

```