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

• Label: 888.2.c
• Level: $888$
• Weight: $2$
• Character orbit: 888.c
• Rep. character: $\chi_{888}(443,\cdot)$
• Character field: $\Q$
• Dimension: $148$
• Newform subspaces: $4$
• Sturm bound: $304$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 888 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(304\)
Trace bound:			\(4\)
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	156	0
Cusp forms	148	148	0
Eisenstein series	8	8	0

Trace form

148 * q - 4 * q^3 - 4 * q^4 - 4 * q^9 + 4 * q^10 - 18 * q^12 + 12 * q^16 - 140 * q^25 - 4 * q^27 + 4 * q^28 - 24 * q^30 + 8 * q^33 - 4 * q^34 + 6 * q^36 + 4 * q^40 - 32 * q^46 - 22 * q^48 - 116 * q^49 + 52 * q^58 - 4 * q^64 + 56 * q^67 + 24 * q^70 - 24 * q^73 - 52 * q^75 - 2 * q^78 - 4 * q^81 + 24 * q^84 - 30 * q^90 + 96 * 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.c.a	$888$	$2$	888.c	888.c	$2$	$16$	$16$	$7.091$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	\(\Q(\sqrt{-111}) \)		✓			888.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{13}q^{2}+\beta _{7}q^{3}-\beta _{15}q^{4}-\beta _{11}q^{5}+\cdots\)
888.2.c.b	$888$	$2$	888.c	888.c	$2$	$16$	$16$	$7.091$	16.0.\(\cdots\).2	None		✓			888.2.c.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{7}q^{3}+(1-\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
888.2.c.c	$888$	$2$	888.c	888.c	$2$	$20$	$20$	$7.091$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	\(\Q(\sqrt{-74}) \)		✓			888.2.c.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-\beta _{12}q^{3}-2q^{4}+\beta _{16}q^{5}+\cdots\)
888.2.c.d	$888$	$2$	888.c	888.c	$2$	$96$	$96$	$7.091$		None		✓	✓		888.2.c.d	$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$