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

• Label: 888.2.f
• Level: $888$
• Weight: $2$
• Character orbit: 888.f
• Rep. character: $\chi_{888}(445,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $304$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(304\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	156	72	84
Cusp forms	148	72	76
Eisenstein series	8	0	8

Trace form

72 * q + 4 * q^4 + 4 * q^6 - 12 * q^8 - 72 * q^9 - 8 * q^10 - 8 * q^12 - 4 * q^14 - 8 * q^15 + 20 * q^16 + 16 * q^20 + 8 * q^24 - 72 * q^25 + 16 * q^26 - 12 * q^28 - 8 * q^31 + 20 * q^34 - 4 * q^36 - 8 * q^38 + 16 * q^39 - 16 * q^40 + 12 * q^42 - 16 * q^44 - 36 * q^46 + 48 * q^47 + 8 * q^48 + 72 * q^49 + 4 * q^50 - 72 * q^52 - 4 * q^54 + 72 * q^56 + 8 * q^58 + 4 * q^60 - 16 * q^62 + 4 * q^64 + 24 * q^66 - 20 * q^68 - 56 * q^70 - 64 * q^71 + 12 * q^72 - 8 * q^76 - 12 * q^78 - 56 * q^79 - 16 * q^80 + 72 * q^81 + 24 * q^82 - 16 * q^84 + 24 * q^86 + 24 * q^87 + 32 * q^88 + 8 * q^90 + 24 * q^92 - 48 * q^94 + 32 * q^95 + 24 * q^96 - 16 * q^97 + 8 * q^98

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.f.a	$888$	$2$	888.f	8.b	$2$	$28$	$28$	$7.091$		None		✓			888.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
888.2.f.b	$888$	$2$	888.f	8.b	$2$	$44$	$44$	$7.091$		None		✓	✓		888.2.f.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(888, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)