Properties

Label 920.2.b
Level $920$
Weight $2$
Character orbit 920.b
Rep. character $\chi_{920}(459,\cdot)$
Character field $\Q$
Dimension $140$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 920 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(920, [\chi])\).

Total New Old
Modular forms 148 148 0
Cusp forms 140 140 0
Eisenstein series 8 8 0

Trace form

\( 140 q + 8 q^{6} - 140 q^{9} + O(q^{10}) \) \( 140 q + 8 q^{6} - 140 q^{9} - 8 q^{16} + 4 q^{24} - 4 q^{25} + 8 q^{26} + 16 q^{35} - 24 q^{36} - 8 q^{41} - 8 q^{46} - 124 q^{49} + 4 q^{50} - 76 q^{54} - 8 q^{59} + 36 q^{64} - 8 q^{70} + 8 q^{75} + 108 q^{81} + 44 q^{94} + 16 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(920, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
920.2.b.a 920.b 920.b $4$ $7.346$ \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+2q^{4}-\beta _{3}q^{5}-2\beta _{3}q^{7}+\cdots\)
920.2.b.b 920.b 920.b $136$ $7.346$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$