Space of modular forms of level 216, weight 3, and Character 216.m

• 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: $1$

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 - 504 * q^77 - 60 * q^79 - 180 * q^83 - 48 * q^85 - 192 * q^91 + 828 * q^95 + 6 * q^97

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
216.3.m.a	$216$	$3$	216.m	9.d	$6$	$4$	$2$	$5.886$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					72.3.m.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-6\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
216.3.m.b	$216$	$3$	216.m	9.d	$6$	$8$	$4$	$5.886$	8.0.\(\cdots\).9	None			✓		72.3.m.b	$2$	$0$	\(0\)	\(0\)	\(6\)	\(6\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)

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

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