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Properties

Label 460.3.f
Level $460$
Weight $3$
Character orbit 460.f
Rep. character $\chi_{460}(321,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $216$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 460.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(460, [\chi])\).

Total New Old
Modular forms 150 16 134
Cusp forms 138 16 122
Eisenstein series 12 0 12

Trace form

\( 16 q + 64 q^{9} - 12 q^{13} - 14 q^{23} - 80 q^{25} + 48 q^{27} + 90 q^{29} + 10 q^{31} + 30 q^{35} + 20 q^{39} + 186 q^{41} - 320 q^{47} + 2 q^{49} - 120 q^{55} - 90 q^{59} - 232 q^{69} - 238 q^{71} - 280 q^{73}+ \cdots + 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(460, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.3.f.a 460.f 23.b $16$ $12.534$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 460.3.f.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(4+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(460, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(460, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)