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 GL(Qp) 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 RepLoc_creation-example (H152E1)

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. 

> 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)
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