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Properties

Label 216.4.q
Level $216$
Weight $4$
Character orbit 216.q
Rep. character $\chi_{216}(25,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $162$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 216.q (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(216, [\chi])\).

Total New Old
Modular forms 672 162 510
Cusp forms 624 162 462
Eisenstein series 48 0 48

Trace form

\( 162 q + O(q^{10}) \) \( 162 q + 75 q^{11} - 132 q^{15} - 204 q^{17} - 60 q^{21} + 156 q^{23} - 447 q^{27} - 126 q^{29} + 261 q^{33} + 1260 q^{35} + 828 q^{39} - 1191 q^{41} + 513 q^{43} - 1674 q^{45} - 1350 q^{47} - 594 q^{49} + 1974 q^{51} + 1908 q^{53} + 225 q^{57} + 966 q^{59} + 54 q^{61} - 1332 q^{63} - 1800 q^{65} + 1161 q^{67} + 96 q^{69} + 2178 q^{75} + 3084 q^{77} - 1092 q^{81} - 1410 q^{83} - 2490 q^{87} - 1089 q^{89} + 936 q^{93} + 3522 q^{95} - 81 q^{97} - 3750 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
216.4.q.a 216.q 27.e $78$ $12.744$ None \(0\) \(0\) \(0\) \(33\) $\mathrm{SU}(2)[C_{9}]$
216.4.q.b 216.q 27.e $84$ $12.744$ None \(0\) \(0\) \(0\) \(-33\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{4}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)