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

\( 204 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} + O(q^{10}) \)

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