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Properties

Label 920.2.bq
Level $920$
Weight $2$
Character orbit 920.bq
Rep. character $\chi_{920}(3,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $2800$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bq (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 920 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 2960 2960 0
Cusp forms 2800 2800 0
Eisenstein series 160 160 0

Trace form

\( 2800 q - 18 q^{2} - 36 q^{3} - 28 q^{6} - 18 q^{8} + O(q^{10}) \) \( 2800 q - 18 q^{2} - 36 q^{3} - 28 q^{6} - 18 q^{8} - 18 q^{10} - 72 q^{11} - 30 q^{12} - 44 q^{16} - 36 q^{17} - 14 q^{18} - 22 q^{20} - 52 q^{22} - 36 q^{25} - 36 q^{26} - 60 q^{27} + 30 q^{28} - 38 q^{30} + 2 q^{32} - 12 q^{33} - 36 q^{35} - 36 q^{36} - 26 q^{38} + 2 q^{40} - 72 q^{41} - 242 q^{42} - 36 q^{43} - 4 q^{46} - 26 q^{48} + 38 q^{50} - 104 q^{51} + 142 q^{52} - 84 q^{56} - 60 q^{57} - 42 q^{58} + 38 q^{60} - 42 q^{62} - 36 q^{65} + 12 q^{66} - 36 q^{67} - 108 q^{68} - 24 q^{70} + 4 q^{72} - 36 q^{73} - 36 q^{75} - 76 q^{76} + 30 q^{78} - 160 q^{80} + 112 q^{81} - 10 q^{82} + 44 q^{83} - 52 q^{86} + 14 q^{88} - 420 q^{90} - 160 q^{91} - 42 q^{92} - 124 q^{96} - 36 q^{97} - 26 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bq.a 920.bq 920.aq $2800$ $7.346$ None \(-18\) \(-36\) \(0\) \(0\) $\mathrm{SU}(2)[C_{44}]$