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

• Label: 888.2.bd
• Level: $888$
• Weight: $2$
• Character orbit: 888.bd
• Rep. character: $\chi_{888}(491,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $296$
• 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.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 888 \)
Character field:			\(\Q(\zeta_{6})\)
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	312	312	0
Cusp forms	296	296	0
Eisenstein series	16	16	0

Trace form

296 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 10 * q^12 + 6 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^22 + 16 * q^24 - 136 * q^25 - 8 * q^27 - 2 * q^28 - 4 * q^30 + 4 * q^33 - 18 * q^34 + 20 * q^36 + 6 * q^40 + 2 * q^42 - 16 * q^43 - 8 * q^46 - 12 * q^48 + 128 * q^49 - 100 * q^51 - 8 * q^52 - 40 * q^54 + 10 * q^57 + 30 * q^58 - 64 * q^60 - 56 * q^64 + 136 * q^66 - 68 * q^67 + 32 * q^70 - 20 * q^72 - 32 * q^73 - 32 * q^75 + 16 * q^76 + 52 * q^78 - 2 * q^81 + 44 * q^82 - 68 * q^84 + 116 * q^88 - 14 * q^90 - 60 * q^91 + 6 * q^94 - 30 * q^96 - 16 * q^99

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.bd.a	$888$	$2$	888.bd	888.ad	$6$	$296$	$148$	$7.091$		None		✓	✓	✓	888.2.bd.a	$8$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$