What are the simplest numerical examples of *even* dihedral (resp. tetrahedral, resp. octahedral, resp. icosahedral) representations

$\rho:\mathrm{Gal}(\bar{\mathbf{Q}}|\mathbf{Q})\to\mathrm{GL}_2(\mathbf{C})$

and their associated Maaß forms $f_\rho\ $ ? The word *simplest* can be taken to mean that the conductor of $\rho$ is small, or a small prime.

[Serre 1977] and [Buzzard 2012] provide many simple examples of *odd* Artin representations $\rho$ of degree $2$ and the associated cuspidal modular forms of weight $1$. For example, the splitting field of $T^3-T-1\ $ gives rise to an odd dihedral representation of conductor $23$ whose associated weight-$1$ modular form is
$$
q\prod_{n>0}(1-q^n)(1-q^{23n}),
$$
as discussed by Emerton in MO11747. For the simplest examples when the image of $\rho$ in $\mathrm{PGL}_2(\mathbf{C})$ is isomorphic to $\mathfrak{A}_4$, $\mathfrak{S}_4$ or $\mathfrak{A}_5$, see [Buzzard 2012].

I'm looking for something similar for even representations. I'm aware of [Vignéras 1985], so my real question is whether there has been further progress in constructing even Artin representations $\rho$ of degree $2$, or the Maaß forms which are supposed to correspond bijectively to such $\rho$ ?

[Buzzard 2012] *Computing weight one modular forms over* $\mathbf{C}$ *and* $\overline{\mathbf{F}}_p$. arXiv:1205.5077.

[Serre 1977] *Modular forms of weight one and Galois representations.* Algebraic number fields: L-functions and Galois properties (Proc. Sympos., Univ. Durham, Durham, 1975), pp. 193–268. Academic Press, London.

[Vignéras 1985] *Représentations galoisiennes paires.* Glasgow Math. J. **27**, 223–237.

**Addendum.** (2012/06/14) Came across the short write-up Explicit Maass Forms by Kevin Buzzard which contains some nice examples.

Numerical computations with the trace formula and the Selberg eigenvalue conjecture.J. Reine Angew. Math. 607 (2007), 113–161. (degruyter.com/view/j/crll.2007.2007.issue-607/crelle.2007.047/…). $\endgroup$ – Chandan Singh Dalawat May 29 '12 at 13:05squarefreeconductor $<3000$ on p.158. If the Artin conjecture is true for even icosahedral representations, then there are only two such representations of squarefree conductor $<3000$; they have conductors $1951$ and $2141$. $\endgroup$ – Chandan Singh Dalawat May 29 '12 at 13:20