Space of modular forms of level 33, weight 6, and Character 33.d

• Label: 33.6.d
• Level: $33$
• Weight: $6$
• Character orbit: 33.d
• Rep. character: $\chi_{33}(32,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(33, [\chi])\).

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

\( 18 q - 23 q^{3} + 252 q^{4} + 253 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(33, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.6.d.a	$33$	$6$	33.d	33.d	$2$	$2$	$2$	$5.293$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(31\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2^{4}-\beta )q^{3}-2^{5}q^{4}+(29-58\beta )q^{5}+\cdots\)
33.6.d.b	$33$	$6$	33.d	33.d	$2$	$16$	$16$	$5.293$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-54\)	\(0\)	\(0\)	$2^{11}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-3-\beta _{2})q^{3}+(20+\beta _{9}+\cdots)q^{4}+\cdots\)