Space of modular forms of level 216, weight 2, and Character 216.n

• Label: 216.2.n
• Level: $216$
• Weight: $2$
• Character orbit: 216.n
• Rep. character: $\chi_{216}(37,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
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	84	28	56
Cusp forms	60	20	40
Eisenstein series	24	8	16

Trace form

20 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 8 * q^10 - 8 * q^14 - q^16 + 8 * q^17 + 16 * q^20 - 5 * q^22 + 14 * q^23 - 20 * q^26 + 4 * q^28 - 2 * q^31 - 19 * q^32 - 9 * q^34 - 25 * q^38 - 2 * q^40 - 2 * q^41 - 42 * q^44 - 12 * q^46 - 18 * q^47 + 25 * q^50 - 28 * q^55 - 26 * q^56 - 14 * q^58 + 68 * q^62 + 26 * q^64 + 22 * q^65 + 39 * q^68 - 16 * q^70 - 48 * q^71 - 8 * q^73 + 34 * q^74 + 9 * q^76 - 2 * q^79 + 96 * q^80 + 18 * q^82 - 29 * q^86 + 19 * q^88 - 8 * q^89 + 30 * q^92 - 40 * q^95 - 2 * q^97 - 102 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(216, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
216.2.n.a	$216$	$2$	216.n	72.n	$6$	$4$	$2$	$1.725$	\(\Q(\zeta_{12})\)	None					72.2.n.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
216.2.n.b	$216$	$2$	216.n	72.n	$6$	$16$	$8$	$1.725$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		72.2.n.b	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(6\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{2}+(\beta _{4}-\beta _{9})q^{4}+(\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(216, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)