Properties

Label 920.2.bk
Level $920$
Weight $2$
Character orbit 920.bk
Rep. character $\chi_{920}(9,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $360$
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.bk (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
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 1520 360 1160
Cusp forms 1360 360 1000
Eisenstein series 160 0 160

Trace form

\( 360q + 32q^{9} + O(q^{10}) \) \( 360q + 32q^{9} + 16q^{11} - 20q^{15} - 16q^{19} - 16q^{21} + 8q^{25} + 12q^{29} + 8q^{31} + 4q^{35} + 52q^{39} - 8q^{41} + 12q^{45} + 102q^{49} + 24q^{51} - 8q^{55} + 34q^{59} - 12q^{65} - 16q^{69} - 8q^{71} + 50q^{75} - 8q^{79} - 236q^{81} + 78q^{85} + 48q^{89} - 248q^{91} + 124q^{95} - 16q^{99} + O(q^{100}) \)

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.bk.a \(360\) \(7.346\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)