Properties

Label 920.2.v
Level $920$
Weight $2$
Character orbit 920.v
Rep. character $\chi_{920}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $264$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 296 264 32
Cusp forms 280 264 16
Eisenstein series 16 0 16

Trace form

\( 264q - 12q^{8} + O(q^{10}) \) \( 264q - 12q^{8} + 16q^{10} - 16q^{12} - 16q^{16} + 8q^{17} - 28q^{18} - 16q^{22} - 8q^{25} - 48q^{26} - 12q^{28} - 24q^{30} + 40q^{32} - 48q^{35} + 32q^{36} + 12q^{38} + 16q^{40} + 40q^{42} - 64q^{43} - 28q^{48} - 40q^{50} + 16q^{52} - 40q^{56} - 20q^{58} - 100q^{60} - 60q^{62} - 8q^{65} - 72q^{66} + 48q^{67} + 72q^{68} - 60q^{70} + 80q^{72} - 40q^{73} + 112q^{75} + 48q^{76} + 28q^{78} - 60q^{80} - 264q^{81} + 44q^{82} + 56q^{86} - 68q^{88} + 64q^{91} + 16q^{96} - 40q^{97} + 16q^{98} + O(q^{100}) \)

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.v.a \(264\) \(7.346\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)