Slopes of the U_7 Operator Acting on a Space of Overconvergent Modular Forms

Details Slopes of the U_7 Operator Acting on a Space of Overconvergent Modular Forms Slopes of the U_7 Operator Acting on a Space of Overconvergent Modular Forms

2011-10-31

arxiv.org/abs/1110.6801v1

Mathematics

Number Theory

Scientific paper

Let \chi\ be the primitive Dirichlet character of conductor 49 defined by \chi(3)=\zeta, for \zeta\ a primitive 42nd root of unity. We explicitly compute the slopes of the U_7 operator acting on the space of overconvergent modular forms on X_1(49) with weight k and character either \chi^{7k-6} or \chi^{8-7k}, depending on the embedding of Q(\zeta) into C_7. By applying results of Coleman, and of Cohen-Oesterl\'e, we are then able to conclude the slopes of U_7 acting on all classical Hecke newforms of the same weight and character.

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