Properties

Label 1911.1.s
Level $1911$
Weight $1$
Character orbit 1911.s
Rep. character $\chi_{1911}(1439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $261$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1911.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(261\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1911, [\chi])\).

Total New Old
Modular forms 50 22 28
Cusp forms 18 6 12
Eisenstein series 32 16 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 4 0 0

Trace form

\( 6 q + q^{3} + 2 q^{4} + 2 q^{6} + q^{9} + O(q^{10}) \) \( 6 q + q^{3} + 2 q^{4} + 2 q^{6} + q^{9} - 2 q^{10} + q^{12} + 5 q^{13} - 2 q^{15} - 2 q^{16} - q^{19} + 2 q^{24} - q^{25} - 2 q^{27} - 4 q^{34} - q^{36} + 2 q^{37} + 2 q^{39} - 2 q^{40} - q^{43} + 4 q^{46} + q^{48} + 2 q^{51} + q^{52} + 4 q^{54} - 2 q^{57} - 2 q^{58} - q^{61} - 2 q^{64} - 2 q^{67} - 2 q^{69} + q^{73} - 2 q^{75} - q^{76} + 2 q^{78} - 4 q^{79} - 3 q^{81} - 2 q^{82} - 2 q^{85} + 4 q^{87} - 4 q^{90} + 4 q^{93} - 2 q^{94} - 3 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1911.1.s.a 1911.s 273.s $2$ $0.954$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{12}+\cdots\)
1911.1.s.b 1911.s 273.s $4$ $0.954$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{4}q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)