Space of modular forms of level 216, weight 3, and Character 216.p

• Label: 216.3.p
• Level: $216$
• Weight: $3$
• Character orbit: 216.p
• Rep. character: $\chi_{216}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(216, [\chi])\).

	Total	New	Old
Modular forms	156	52	104
Cusp forms	132	44	88
Eisenstein series	24	8	16

Trace form

\( 44 q + q^{2} - q^{4} - 14 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(216, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
216.3.p.a	$216$	$3$	216.p	72.p	$6$	$4$	$2$	$5.886$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{3}$	$\mathrm{U}(1)[D_{6}]$	\(q-2\beta _{1}q^{2}+(-4+4\beta _{1})q^{4}+8q^{8}+\cdots\)
216.3.p.b	$216$	$3$	216.p	72.p	$6$	$40$	$20$	$5.886$		None		$4$	$0$	\(5\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)