Properties

Label 920.2.j
Level $920$
Weight $2$
Character orbit 920.j
Rep. character $\chi_{920}(829,\cdot)$
Character field $\Q$
Dimension $132$
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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
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 148 132 16
Cusp forms 140 132 8
Eisenstein series 8 0 8

Trace form

\( 132q + 132q^{9} + O(q^{10}) \) \( 132q + 132q^{9} - 14q^{10} - 20q^{14} + 8q^{16} - 8q^{20} - 44q^{24} + 4q^{25} + 8q^{26} + 14q^{30} - 24q^{31} + 8q^{34} - 56q^{36} - 32q^{39} + 6q^{40} - 8q^{41} + 36q^{44} - 132q^{49} - 12q^{50} - 12q^{54} - 32q^{55} - 36q^{56} - 48q^{60} - 60q^{64} - 24q^{65} - 32q^{66} + 28q^{70} + 88q^{71} + 44q^{74} - 84q^{76} + 54q^{80} + 132q^{81} + 108q^{84} - 68q^{86} - 40q^{89} + 20q^{90} - 12q^{94} + 24q^{95} + 24q^{96} + O(q^{100}) \)

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.j.a \(132\) \(7.346\) None \(0\) \(0\) \(0\) \(0\)

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

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