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Properties

Label 920.1.bh
Level $920$
Weight $1$
Character orbit 920.bh
Rep. character $\chi_{920}(59,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $20$
Newform subspaces $2$
Sturm bound $144$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 920.bh (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 920 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(920, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q - 2 q^{4} - 2 q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{14} - 2 q^{16} - 4 q^{19} - 2 q^{25} - 4 q^{26} + 18 q^{35} - 2 q^{36} - 2 q^{40} - 4 q^{41} - 4 q^{44} - 2 q^{46} - 6 q^{49} - 4 q^{56} + 18 q^{59}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(920, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
920.1.bh.a 920.bh 920.ah $10$ $0.459$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-10}) \) None 920.1.bh.a \(-1\) \(0\) \(-1\) \(-2\) \(q-\zeta_{22}q^{2}+\zeta_{22}^{2}q^{4}+\zeta_{22}^{6}q^{5}+(-\zeta_{22}^{3}+\cdots)q^{7}+\cdots\)
920.1.bh.b 920.bh 920.ah $10$ $0.459$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-10}) \) None 920.1.bh.a \(1\) \(0\) \(1\) \(2\) \(q+\zeta_{22}q^{2}+\zeta_{22}^{2}q^{4}-\zeta_{22}^{6}q^{5}+(\zeta_{22}^{3}+\cdots)q^{7}+\cdots\)