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Properties

Label 216.9.m
Level $216$
Weight $9$
Character orbit 216.m
Rep. character $\chi_{216}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $324$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 216.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(324\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(216, [\chi])\).

Total New Old
Modular forms 600 48 552
Cusp forms 552 48 504
Eisenstein series 48 0 48

Trace form

\( 48 q + 11592 q^{11} - 177072 q^{19} + 689760 q^{23} + 1875000 q^{25} + 2846448 q^{29} - 214176 q^{31} - 5246712 q^{41} - 4864824 q^{43} + 14112144 q^{47} - 23547528 q^{49} + 13193184 q^{55} + 2459016 q^{59}+ \cdots - 60511080 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
216.9.m.a 216.m 9.d $48$ $87.994$ None 72.9.m.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{9}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(216, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)