Space of modular forms of level 33, weight 5, and Character 33.c

• Label: 33.5.c
• Level: $33$
• Weight: $5$
• Character orbit: 33.c
• Rep. character: $\chi_{33}(10,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(33, [\chi])\).

	Total	New	Old
Modular forms	18	8	10
Cusp forms	14	8	6
Eisenstein series	4	0	4

Trace form

\( 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(33, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.5.c.a	$33$	$5$	33.c	11.b	$2$	$8$	$8$	$3.411$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-36\)	\(0\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-10-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)