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Properties

Label 468.2.bm
Level $468$
Weight $2$
Character orbit 468.bm
Rep. character $\chi_{468}(263,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 468.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 468 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).

Total New Old
Modular forms 176 176 0
Cusp forms 160 160 0
Eisenstein series 16 16 0

Trace form

\( 160 q - 2 q^{4} - 12 q^{5} - 6 q^{6} - 2 q^{9} - 4 q^{10} - 7 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} + 4 q^{18} - 3 q^{20} - 2 q^{21} - 18 q^{22} + 12 q^{24} + 60 q^{25} - 18 q^{26} + 6 q^{28} - 18 q^{30}+ \cdots - 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
468.2.bm.a 468.bm 468.am $160$ $3.737$ None 468.2.bd.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$