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

• Label: 33.5.g
• Level: $33$
• Weight: $5$
• Character orbit: 33.g
• Rep. character: $\chi_{33}(7,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.g (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
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	72	32	40
Cusp forms	56	32	24
Eisenstein series	16	0	16

Trace form

\( 32 q + 76 q^{4} + 36 q^{5} + 150 q^{7} + 480 q^{8} - 216 q^{9} + O(q^{10}) \)

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.g.a	$33$	$5$	33.g	11.d	$10$	$32$	$8$	$3.411$		None		$2$	$0$	\(0\)	\(0\)	\(36\)	\(150\)		$\mathrm{SU}(2)[C_{10}]$

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

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