Space of modular forms of level 888, weight 2, and Character 888.o

• Label: 888.2.o
• Level: $888$
• Weight: $2$
• Character orbit: 888.o
• Rep. character: $\chi_{888}(517,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $304$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(304\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(888, [\chi])\).

	Total	New	Old
Modular forms	156	76	80
Cusp forms	148	76	72
Eisenstein series	8	0	8

Trace form

76 * q + 4 * q^4 + 8 * q^7 - 76 * q^9 + 4 * q^16 + 84 * q^25 + 12 * q^28 + 8 * q^30 - 12 * q^34 - 4 * q^36 + 8 * q^38 - 56 * q^40 - 8 * q^41 - 24 * q^44 - 44 * q^46 - 8 * q^48 + 60 * q^49 - 40 * q^58 + 32 * q^62 - 8 * q^63 + 4 * q^64 + 48 * q^65 - 32 * q^70 - 16 * q^71 + 24 * q^73 - 44 * q^74 - 44 * q^78 + 76 * q^81 + 16 * q^84 - 56 * q^86

Decomposition of \(S_{2}^{\mathrm{new}}(888, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
888.2.o.a	$888$	$2$	888.o	296.e	$2$	$76$	$76$	$7.091$		None		✓	✓	✓	888.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(888, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(888, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)