Properties

Label 460.2.x
Level $460$
Weight $2$
Character orbit 460.x
Rep. character $\chi_{460}(17,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $240$
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.x (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
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 1560 240 1320
Cusp forms 1320 240 1080
Eisenstein series 240 0 240

Trace form

\( 240q + 4q^{3} + O(q^{10}) \) \( 240q + 4q^{3} - 8q^{13} + 46q^{23} - 24q^{25} - 20q^{27} + 12q^{31} + 22q^{33} + 4q^{35} - 88q^{37} + 12q^{41} - 92q^{47} - 36q^{55} - 88q^{57} + 88q^{61} + 168q^{71} + 20q^{73} + 12q^{75} + 36q^{77} + 200q^{81} - 28q^{85} + 16q^{87} - 88q^{93} - 86q^{95} - 66q^{97} + O(q^{100}) \)

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.x.a \(240\) \(3.673\) None \(0\) \(4\) \(0\) \(0\)

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

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