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Properties

Label 216.2.q
Level $216$
Weight $2$
Character orbit 216.q
Rep. character $\chi_{216}(25,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $54$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
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: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(216, [\chi])\).

Total New Old
Modular forms 240 54 186
Cusp forms 192 54 138
Eisenstein series 48 0 48

Trace form

\( 54 q + O(q^{10}) \) \( 54 q + 3 q^{11} + 12 q^{15} + 12 q^{17} + 12 q^{21} + 12 q^{23} - 15 q^{27} - 18 q^{29} - 9 q^{33} - 36 q^{35} - 36 q^{39} - 21 q^{41} + 9 q^{43} - 54 q^{45} - 54 q^{47} + 18 q^{49} - 42 q^{51} - 36 q^{53} - 45 q^{57} - 42 q^{59} + 18 q^{61} - 36 q^{63} - 72 q^{65} + 9 q^{67} - 48 q^{69} + 18 q^{75} - 12 q^{77} - 12 q^{81} + 30 q^{83} + 30 q^{87} + 45 q^{89} + 72 q^{93} + 138 q^{95} - 27 q^{97} + 138 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
216.2.q.a 216.q 27.e $24$ $1.725$ None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$
216.2.q.b 216.q 27.e $30$ $1.725$ None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

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