Properties

Label 468.2.bl
Level $468$
Weight $2$
Character orbit 468.bl
Rep. character $\chi_{468}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 468.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 180 28 152
Cusp forms 156 28 128
Eisenstein series 24 0 24

Trace form

\( 28 q + 8 q^{9} + O(q^{10}) \) \( 28 q + 8 q^{9} - q^{13} + 16 q^{17} - 8 q^{23} + 14 q^{25} - 18 q^{27} + 26 q^{29} - 8 q^{35} + 19 q^{39} - 4 q^{43} + 16 q^{49} - 8 q^{51} - 14 q^{61} + 7 q^{65} + 16 q^{69} - 64 q^{75} - 14 q^{79} - 16 q^{81} - 40 q^{87} + 6 q^{91} - 24 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
468.2.bl.a 468.bl 117.t $4$ $3.737$ \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
468.2.bl.b 468.bl 117.t $24$ $3.737$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(468, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(468, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)