Space of modular forms of level 33, weight 2, and Character 33.d

• Label: 33.2.d
• Level: $33$
• Weight: $2$
• Character orbit: 33.d
• Rep. character: $\chi_{33}(32,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(33, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(33, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.2.d.a	$33$	$2$	33.d	33.d	$2$	$2$	$2$	$0.264$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)