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

• Label: 33.8.e
• Level: $33$
• Weight: $8$
• Character orbit: 33.e
• Rep. character: $\chi_{33}(4,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	120	56	64
Cusp forms	104	56	48
Eisenstein series	16	0	16

Trace form

\( 56 q - 28 q^{2} - 532 q^{4} - 4 q^{5} + 432 q^{6} + 1206 q^{7} + 6524 q^{8} - 10206 q^{9} + O(q^{10}) \)

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.e.a	$33$	$8$	33.e	11.c	$5$	$28$	$7$	$10.309$		None		$2$	$0$	\(-22\)	\(189\)	\(-777\)	\(-83\)		$\mathrm{SU}(2)[C_{5}]$
33.8.e.b	$33$	$8$	33.e	11.c	$5$	$28$	$7$	$10.309$		None		$2$	$0$	\(-6\)	\(-189\)	\(773\)	\(1289\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{8}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)