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

• Label: 216.2.v
• Level: $216$
• Weight: $2$
• Character orbit: 216.v
• Rep. character: $\chi_{216}(11,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $204$
• 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.v (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 216 \)
Character field:			\(\Q(\zeta_{18})\)
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	228	228	0
Cusp forms	204	204	0
Eisenstein series	24	24	0

Trace form

204 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 15 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 15 * q^18 - 6 * q^19 - 27 * q^20 - 6 * q^22 - 30 * q^24 - 12 * q^25 - 12 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 24 * q^33 - 12 * q^34 - 18 * q^35 - 36 * q^36 - 30 * q^38 + 9 * q^40 - 6 * q^42 - 12 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 30 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 + 6 * q^57 - 33 * q^58 - 48 * q^59 - 54 * q^60 + 90 * q^62 - 3 * q^64 - 12 * q^65 + 87 * q^66 - 12 * q^67 - 9 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 6 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 78 * q^86 - 30 * q^88 - 18 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 + 18 * q^96 - 12 * q^97 + 162 * q^98 - 12 * q^99

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.v.a	$216$	$2$	216.v	216.v	$18$	$12$	$2$	$1.725$	12.0.\(\cdots\).1	\(\Q(\sqrt{-2}) \)		✓			216.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q-\beta _{11}q^{2}+(\beta _{5}-\beta _{8}-\beta _{11})q^{3}-2\beta _{4}q^{4}+\cdots\)
216.2.v.b	$216$	$2$	216.v	216.v	$18$	$192$	$32$	$1.725$		None		✓	✓		216.2.v.b	$4$	$0$	\(-6\)	\(-12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$