Properties

Label 216.3.m
Level $216$
Weight $3$
Character orbit 216.m
Rep. character $\chi_{216}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(216, [\chi])\).

Total New Old
Modular forms 168 12 156
Cusp forms 120 12 108
Eisenstein series 48 0 48

Trace form

\( 12 q - 18 q^{11} + 12 q^{19} + 72 q^{23} + 30 q^{25} + 108 q^{29} + 24 q^{31} - 126 q^{41} - 18 q^{43} - 324 q^{47} - 18 q^{49} - 24 q^{55} + 126 q^{59} - 48 q^{61} + 432 q^{65} - 42 q^{67} - 36 q^{73}+ \cdots + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
216.3.m.a 216.m 9.d $4$ $5.886$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 72.3.m.a \(0\) \(0\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
216.3.m.b 216.m 9.d $8$ $5.886$ 8.0.\(\cdots\).9 None 72.3.m.b \(0\) \(0\) \(6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

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