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Properties

Label 201.1.k
Level $201$
Weight $1$
Character orbit 201.k
Rep. character $\chi_{201}(14,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $10$
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.k (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q(\zeta_{22})\)
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 30 30 0
Cusp forms 10 10 0
Eisenstein series 20 20 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 10 0 0 0

Trace form

\( 10 q - q^{3} - q^{4} - 2 q^{7} - q^{9} + O(q^{10}) \) \( 10 q - q^{3} - q^{4} - 2 q^{7} - q^{9} - q^{12} - 2 q^{13} - q^{16} - 2 q^{19} - 2 q^{21} - q^{25} - q^{27} - 2 q^{28} - 2 q^{31} - q^{36} - 2 q^{37} - 2 q^{39} - 2 q^{43} - q^{48} - 3 q^{49} + 9 q^{52} + 9 q^{57} - 2 q^{61} + 9 q^{63} - q^{64} - q^{67} + 9 q^{73} - q^{75} - 2 q^{76} + 9 q^{79} - q^{81} + 9 q^{84} - 4 q^{91} - 2 q^{93} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.k.a 201.k 201.k $10$ $0.100$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{22}^{7}q^{3}+\zeta_{22}^{6}q^{4}+(\zeta_{22}^{8}-\zeta_{22}^{9}+\cdots)q^{7}+\cdots\)