Properties

Label 1911.1.w
Level $1911$
Weight $1$
Character orbit 1911.w
Rep. character $\chi_{1911}(116,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $6$
Sturm bound $261$
Trace bound $3$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 60 44 16
Cusp forms 28 28 0
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 28 0 0 0

Trace form

\( 28 q - 10 q^{4} - 14 q^{9} + O(q^{10}) \) \( 28 q - 10 q^{4} - 14 q^{9} - 6 q^{16} - 16 q^{22} - 10 q^{25} + 8 q^{30} + 20 q^{36} + 2 q^{39} - 8 q^{43} + 4 q^{64} + 4 q^{79} - 14 q^{81} + 16 q^{88} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1911.1.w.a $2$ $0.954$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{12}+\cdots\)
1911.1.w.b $2$ $0.954$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
1911.1.w.c $4$ $0.954$ \(\Q(\sqrt{2}, \sqrt{-3})\) $D_{4}$ \(\Q(\sqrt{-39}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
1911.1.w.d $4$ $0.954$ \(\Q(\sqrt{2}, \sqrt{-3})\) $D_{4}$ \(\Q(\sqrt{-39}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots\)
1911.1.w.e $8$ $0.954$ 8.0.339738624.2 $D_{8}$ \(\Q(\sqrt{-39}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{5}q^{3}+(\beta _{5}-\beta _{6})q^{4}+\beta _{1}q^{5}+\cdots\)
1911.1.w.f $8$ $0.954$ 8.0.339738624.2 $D_{8}$ \(\Q(\sqrt{-39}) \) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{5}q^{3}+(\beta _{5}-\beta _{6})q^{4}-\beta _{1}q^{5}+\cdots\)