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

• Label: 333.3.bg
• Level: $333$
• Weight: $3$
• Character orbit: 333.bg
• Rep. character: $\chi_{333}(88,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $296$
• 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.bg (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{12})\)
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	312	312	0
Cusp forms	296	296	0
Eisenstein series	16	16	0

Trace form

\( 296 q - 2 q^{2} - 6 q^{3} - 6 q^{4} + 4 q^{5} + 12 q^{6} - 4 q^{7} - 12 q^{9} + O(q^{10}) \)

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.bg.a	$333$	$3$	333.bg	333.ag	$12$	$296$	$74$	$9.074$		None		✓	✓	✓	333.3.ba.a	$2$	$0$	\(-2\)	\(-6\)	\(4\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$