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Properties

Label 460.2.s
Level $460$
Weight $2$
Character orbit 460.s
Rep. character $\chi_{460}(9,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $120$
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.s (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
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 780 120 660
Cusp forms 660 120 540
Eisenstein series 120 0 120

Trace form

\( 120 q + 20 q^{9} + O(q^{10}) \) \( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.2.s.a 460.s 115.j $120$ $3.673$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

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

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