Properties

Label 460.2.q
Level $460$
Weight $2$
Character orbit 460.q
Rep. character $\chi_{460}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $480$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.q (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(460, [\chi])\).

Total New Old
Modular forms 760 480 280
Cusp forms 680 480 200
Eisenstein series 80 0 80

Trace form

\( 480q - 4q^{2} + 2q^{6} + 2q^{8} + 48q^{9} + O(q^{10}) \) \( 480q - 4q^{2} + 2q^{6} + 2q^{8} + 48q^{9} + 6q^{12} - 24q^{16} + 26q^{18} + 4q^{24} + 48q^{25} - 14q^{26} + 40q^{29} + 16q^{32} - 22q^{34} - 152q^{36} - 110q^{38} - 88q^{40} - 8q^{41} - 22q^{44} - 132q^{46} - 190q^{48} - 56q^{49} - 18q^{50} - 50q^{52} - 90q^{54} - 110q^{56} - 136q^{58} - 22q^{60} + 30q^{62} - 30q^{64} + 4q^{69} + 110q^{72} + 22q^{74} - 176q^{77} + 66q^{78} - 8q^{81} + 154q^{82} + 308q^{84} + 32q^{85} + 176q^{88} - 88q^{89} + 134q^{92} - 448q^{93} + 204q^{94} + 6q^{96} - 88q^{97} + 132q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(460, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
460.2.q.a \(480\) \(3.673\) None \(-4\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(460, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(460, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)