The file ReducedPolynomials lists the reduced polynomials corresponding to mod-l projective representations
associated to discriminant modular forms, i.e. unique newform of level one weight 12,16,18,20,22 or 26.

The 13 cases with (weight,level)=(12,11),(12,13),(12,17),(12,19),(16,17),(16,19),(16,23),(18,17),(18,19),(18,23),(20,19),(20,23),(22,23)
were first computed by Johan Bosman, see Chapter 7 of the book:
S. J. Edixhoven and J.-M. Couveignes (with R. S. de Jong, F. Merkl and J. G.
Bosman), Computational Aspects of Modular Forms and Galois Representations, Annals of
Mathematics Studies 176, Princeton University Press, 2011.

The entire Galois representation for (12,29) was first computed by Nicolas Mascot, see:
N. Mascot, Computing modular Galois representations, http://arxiv.org/abs/1211.1635v2

The case (12,31) was first computed by Jinxiang Zeng and Linsheng Yin, see:
J. Zeng and L. Yin, On the computation of coefficients of modular forms: the reduction modulo p approach, http://arxiv.org/abs/1211.1124v4

The 3 cases with (weight,level)=(16,29),(20,31),(22,31) are first computed by Peng Tian, see:
P. Tian, Further computations of Galois Representations associated to modular forms, http://arxiv.org/abs/1311.0577v1

The 14 cases with (weight,level)=(12,41),(16,43),(18,29),(18,37),(18,41),(20,37),
(22,29),(22,37),(22,41),(26,29),(26,31),(26,37),(26,41) are first computed by 
Maarten Derickx, Mark van Hoeij and Jinxiang Zeng, see:
M. Derickx, M. van Hoeij and J. Zeng, Computing Galois Representations and Equations for Modular Curves $X_H(\ell)$.


At the moment, the mod-p approach can handle more significantly more cases than the floating
point approach (of course, future progress may change this). The highest l reached by floating
point methods is l=31  (two cases: (20,31) and (22,31)). With the mod-p method, we have computed:
	4 cases for l=31,
	4 cases for l=37,
	4 cases for l=41, and
	1 case  for l=43.
For completeness, we also recomputed the cases done with the floating point approach so
that we can list those as well.

The smallest not-yet computed case is (12,37). Without additional algorithmic improvements
it is not clear how to tackle this case.