Properties

Label 1156.1.g
Level $1156$
Weight $1$
Character orbit 1156.g
Rep. character $\chi_{1156}(155,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $12$
Newform subspaces $2$
Sturm bound $153$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1156 = 2^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1156.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(153\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1156, [\chi])\).

Total New Old
Modular forms 84 68 16
Cusp forms 12 12 0
Eisenstein series 72 56 16

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + O(q^{10}) \) \( 12 q - 12 q^{16} - 4 q^{18} + 12 q^{50} - 8 q^{52} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1156, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1156.1.g.a \(4\) \(0.577\) \(\Q(\zeta_{8})\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\)
1156.1.g.b \(8\) \(0.577\) \(\Q(\zeta_{16})\) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-\zeta_{16}^{3}-\zeta_{16}^{7}+\cdots)q^{5}+\cdots\)