Space of modular forms of level 228, weight 3, and Character 228.x

• Label: 228.3.x
• Level: $228$
• Weight: $3$
• Character orbit: 228.x
• Rep. character: $\chi_{228}(43,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $240$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.x (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(228, [\chi])\).

	Total	New	Old
Modular forms	504	240	264
Cusp forms	456	240	216
Eisenstein series	48	0	48

Trace form

\( 240 q - 6 q^{4} - 18 q^{6} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(228, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
228.3.x.a	$228$	$3$	228.x	76.l	$18$	$120$	$20$	$6.213$		None		$2$	$0$	\(-9\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
228.3.x.b	$228$	$3$	228.x	76.l	$18$	$120$	$20$	$6.213$		None		$2$	$0$	\(9\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)