Properties

Label 460.2.j
Level $460$
Weight $2$
Character orbit 460.j
Rep. character $\chi_{460}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $132$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
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 152 132 20
Cusp forms 136 132 4
Eisenstein series 16 0 16

Trace form

\( 132q - 12q^{8} + O(q^{10}) \) \( 132q - 12q^{8} - 16q^{10} - 16q^{12} - 4q^{13} + 16q^{16} - 20q^{17} + 28q^{18} - 16q^{22} - 20q^{25} - 16q^{26} + 12q^{28} - 24q^{30} - 40q^{32} + 16q^{33} - 32q^{36} + 20q^{37} - 12q^{38} - 16q^{40} - 40q^{42} + 20q^{45} + 28q^{48} + 40q^{50} + 16q^{52} + 4q^{53} + 40q^{56} + 20q^{58} + 20q^{60} + 60q^{62} + 20q^{65} + 40q^{66} - 16q^{68} - 60q^{70} + 40q^{72} + 36q^{73} - 48q^{76} + 28q^{78} - 60q^{80} - 132q^{81} - 44q^{82} - 20q^{85} - 88q^{86} + 28q^{88} + 120q^{90} - 96q^{96} - 60q^{97} - 80q^{98} + O(q^{100}) \)

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.j.a \(132\) \(3.673\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(460, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)