Properties

Label 1911.1.be
Level $1911$
Weight $1$
Character orbit 1911.be
Rep. character $\chi_{1911}(932,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $4$
Sturm bound $261$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1911.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(261\)
Trace bound: \(6\)

Dimensions

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

Total New Old
Modular forms 44 32 12
Cusp forms 12 12 0
Eisenstein series 32 20 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 8 0 0

Trace form

\( 12 q - 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 12 q - 2 q^{4} + 2 q^{9} - 4 q^{15} + 2 q^{16} + 4 q^{25} - 2 q^{36} - 2 q^{37} - 2 q^{39} - 2 q^{43} - 4 q^{46} - 8 q^{51} - 4 q^{57} - 4 q^{58} - 4 q^{64} - 4 q^{67} + 4 q^{78} + 16 q^{79} - 6 q^{81} - 4 q^{85} - 4 q^{93} + O(q^{100}) \)

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.be.a 1911.be 39.i $2$ $0.954$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}+q^{12}+\cdots\)
1911.1.be.b 1911.be 39.i $2$ $0.954$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots\)
1911.1.be.c 1911.be 39.i $4$ $0.954$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)
1911.1.be.d 1911.be 39.i $4$ $0.954$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}^{3}q^{5}+\cdots\)