Space of modular forms of level 216, weight 4, and Character 216.f

• Label: 216.4.f
• Level: $216$
• Weight: $4$
• Character orbit: 216.f
• Rep. character: $\chi_{216}(107,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(216, [\chi])\).

	Total	New	Old
Modular forms	114	48	66
Cusp forms	102	48	54
Eisenstein series	12	0	12

Trace form

\( 48 q + 6 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(216, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
216.4.f.a	$216$	$4$	216.f	24.f	$2$	$24$	$24$	$12.744$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
216.4.f.b	$216$	$4$	216.f	24.f	$2$	$24$	$24$	$12.744$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)