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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

\( 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9} + 6 q^{12} - 24 q^{16} + 26 q^{18} + 4 q^{24} + 48 q^{25} - 14 q^{26} + 40 q^{29} + 16 q^{32} - 22 q^{34} - 152 q^{36} - 110 q^{38} - 88 q^{40} - 8 q^{41}+ \cdots + 132 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.2.q.a 460.q 92.h $480$ $3.673$ None 460.2.q.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

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

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