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

• Label: 888.2.j
• Level: $888$
• Weight: $2$
• Character orbit: 888.j
• Rep. character: $\chi_{888}(371,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $3$
• Sturm bound: $304$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(304\)
Trace bound:			\(2\)
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	144	12
Cusp forms	148	144	4
Eisenstein series	8	0	8

Trace form

144 * q + 4 * q^4 - 6 * q^6 - 12 * q^10 - 6 * q^12 - 4 * q^16 - 6 * q^18 - 16 * q^19 + 4 * q^22 + 144 * q^25 - 24 * q^27 + 20 * q^28 - 20 * q^30 - 8 * q^33 - 20 * q^34 - 34 * q^36 - 12 * q^40 + 22 * q^42 + 32 * q^43 - 16 * q^46 + 22 * q^48 - 144 * q^49 + 32 * q^52 - 4 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 + 76 * q^64 + 10 * q^66 + 40 * q^70 - 72 * q^72 + 14 * q^78 + 24 * q^81 + 68 * q^82 - 52 * q^84 - 64 * q^88 - 58 * q^90 + 48 * q^91 + 12 * q^94 + 4 * q^96 + 16 * q^97

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.j.a	$888$	$2$	888.j	24.f	$2$	$4$	$4$	$7.091$	\(\Q(\zeta_{12})\)	None		✓			888.2.j.a	$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{3}-\beta_{2})q^{2}+(\beta_{3}-\beta_1+1)q^{3}+\cdots\)
888.2.j.b	$888$	$2$	888.j	24.f	$2$	$4$	$4$	$7.091$	\(\Q(\zeta_{12})\)	None		✓			888.2.j.a	$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{3}+1)q^{2}+(\beta_{3}-\beta_1+1)q^{3}+\cdots\)
888.2.j.c	$888$	$2$	888.j	24.f	$2$	$136$	$136$	$7.091$		None		✓	✓		888.2.j.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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