Space of modular forms of level 33, weight 8, and Character 33.f

• Label: 33.8.f
• Level: $33$
• Weight: $8$
• Character orbit: 33.f
• Rep. character: $\chi_{33}(2,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $104$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.f (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(33, [\chi])\).

	Total	New	Old
Modular forms	120	120	0
Cusp forms	104	104	0
Eisenstein series	16	16	0

Trace form

\( 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(33, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.8.f.a	$33$	$8$	33.f	33.f	$10$	$104$	$26$	$10.309$		None		$4$	$0$	\(0\)	\(-42\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{10}]$