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

• Label: 216.2.l
• Level: $216$
• Weight: $2$
• Character orbit: 216.l
• Rep. character: $\chi_{216}(35,\cdot)$
• 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.l (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 + 3 * q^2 - q^4 + 6 * q^11 + 18 * q^14 - q^16 - 8 * q^19 - 18 * q^20 - 5 * q^22 - 4 * q^25 - 12 * q^28 - 27 * q^32 - 5 * q^34 - 21 * q^38 - 12 * q^40 + 18 * q^41 - 2 * q^43 + 12 * q^46 - 4 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 30 * q^59 + 2 * q^64 + 6 * q^65 - 2 * q^67 + 45 * q^68 + 18 * q^70 - 8 * q^73 + 60 * q^74 - 11 * q^76 + 10 * q^82 - 54 * q^83 + 87 * q^86 - 5 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 - 2 * q^97

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.l.a	$216$	$2$	216.l	72.l	$6$	$4$	$2$	$1.725$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)					72.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{3}q^{8}+(3-\beta _{1}+\cdots)q^{11}+\cdots\)
216.2.l.b	$216$	$2$	216.l	72.l	$6$	$16$	$8$	$1.725$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		72.2.l.b	$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{11}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)

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

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