Properties

Label 201.1.g
Level $201$
Weight $1$
Character orbit 201.g
Rep. character $\chi_{201}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 201.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(201, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4 q - 2 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{6} - 2 q^{7} - 4 q^{9} - 2 q^{13} + 2 q^{16} + 2 q^{19} - 4 q^{22} + 4 q^{24} + 4 q^{25} + 2 q^{31} - 2 q^{33} + 2 q^{34} - 2 q^{37} + 4 q^{42} - 2 q^{46} - 2 q^{51} + 2 q^{54} - 4 q^{58} - 2 q^{61} + 2 q^{63} - 4 q^{64} - 4 q^{67} + 2 q^{69} + 2 q^{73} - 2 q^{78} - 2 q^{79} + 4 q^{81} + 4 q^{82} - 2 q^{87} + 2 q^{88} + 4 q^{91} - 4 q^{94} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(201, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
201.1.g.a 201.g 201.g $4$ $0.100$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{6}+\cdots\)