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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
920.2.bq.a \(2800\) \(7.346\) None \(-18\) \(-36\) \(0\) \(0\)