Properties

Label 567.2.be
Level $567$
Weight $2$
Character orbit 567.be
Rep. character $\chi_{567}(62,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $132$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(567, [\chi])\).

Total New Old
Modular forms 468 156 312
Cusp forms 396 132 264
Eisenstein series 72 24 48

Trace form

\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + O(q^{10}) \) \( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44} - 6 q^{46} - 24 q^{49} - 18 q^{50} - 57 q^{56} - 12 q^{58} + 18 q^{64} - 78 q^{65} - 12 q^{67} - 69 q^{70} - 18 q^{71} + 6 q^{74} + 57 q^{77} + 24 q^{79} + 54 q^{85} + 42 q^{86} - 72 q^{88} + 6 q^{91} + 120 q^{92} - 126 q^{95} - 126 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
567.2.be.a 567.be 189.ae $132$ $4.528$ None \(12\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)