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

\( 12q + O(q^{10}) \) \( 12q - 18q^{11} + 12q^{19} + 72q^{23} + 30q^{25} + 108q^{29} + 24q^{31} - 126q^{41} - 18q^{43} - 324q^{47} - 18q^{49} - 24q^{55} + 126q^{59} - 48q^{61} + 432q^{65} - 42q^{67} - 36q^{73} - 504q^{77} - 60q^{79} - 180q^{83} - 48q^{85} - 192q^{91} + 828q^{95} + 6q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
216.3.m.a \(4\) \(5.886\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-6\) \(-6\) \(q+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
216.3.m.b \(8\) \(5.886\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(6\) \(6\) \(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)

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

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