Space of modular forms of level 33, weight 9, and Character 33.b

• Label: 33.9.b
• Level: $33$
• Weight: $9$
• Character orbit: 33.b
• Rep. character: $\chi_{33}(23,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(33, [\chi])\).

	Total	New	Old
Modular forms	34	26	8
Cusp forms	30	26	4
Eisenstein series	4	0	4

Trace form

\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(33, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.9.b.a	$33$	$9$	33.b	3.b	$2$	$26$	$26$	$13.443$		None		$2$	$0$	\(0\)	\(-35\)	\(0\)	\(7156\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)