Properties

Label 1911.1.bc
Level $1911$
Weight $1$
Character orbit 1911.bc
Rep. character $\chi_{1911}(491,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
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 36 24 12
Cusp forms 4 4 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 0 0 0

Trace form

\( 4 q + 2 q^{4} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} - 2 q^{9} - 2 q^{16} - 4 q^{25} + 2 q^{36} + 6 q^{37} - 2 q^{39} + 2 q^{43} - 4 q^{64} - 8 q^{79} - 2 q^{81} + O(q^{100}) \)

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.bc.a 1911.bc 39.h $2$ $0.954$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}-q^{12}+\cdots\)
1911.1.bc.b 1911.bc 39.h $2$ $0.954$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots\)