Properties

Label 1161.1.bz
Level $1161$
Weight $1$
Character orbit 1161.bz
Rep. character $\chi_{1161}(28,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1161 = 3^{3} \cdot 43 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1161.bz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1161, [\chi])\).

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

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

\( 12 q - 2 q^{4} + O(q^{10}) \) \( 12 q - 2 q^{4} + q^{13} - 2 q^{16} - 3 q^{19} + q^{25} + 8 q^{31} + 2 q^{43} + 8 q^{49} - 13 q^{52} + 3 q^{61} - 2 q^{64} - 2 q^{67} - 3 q^{76} + q^{79} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1161, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1161.1.bz.a 1161.bz 43.h $12$ $0.579$ \(\Q(\zeta_{21})\) $D_{42}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{42}^{3}q^{4}+(-\zeta_{42}+\zeta_{42}^{13})q^{7}+\cdots\)