Space of modular forms of level 333, weight 3, and Character 333.bj

• Label: 333.3.bj
• Level: $333$
• Weight: $3$
• Character orbit: 333.bj
• Rep. character: $\chi_{333}(95,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $444$
• Newform subspaces: $1$
• Sturm bound: $114$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.bj (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(114\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(333, [\chi])\).

	Total	New	Old
Modular forms	468	468	0
Cusp forms	444	444	0
Eisenstein series	24	24	0

Trace form

\( 444 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(333, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
333.3.bj.a	$333$	$3$	333.bj	333.aj	$18$	$444$	$74$	$9.074$		None		✓	✓	✓	333.3.bh.a	$2$	$0$	\(-9\)	\(0\)	\(-9\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$