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

• Label: 888.2.r
• Level: $888$
• Weight: $2$
• Character orbit: 888.r
• Rep. character: $\chi_{888}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $152$
• Newform subspaces: $6$
• Sturm bound: $304$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(304\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	312	152	160
Cusp forms	296	152	144
Eisenstein series	16	0	16

Trace form

152 * q + 4 * q^2 + 4 * q^8 - 152 * q^9 + 4 * q^14 + 8 * q^16 + 8 * q^17 - 4 * q^18 - 8 * q^22 + 24 * q^32 + 16 * q^34 + 96 * q^38 - 20 * q^42 + 16 * q^43 + 40 * q^44 - 16 * q^46 - 120 * q^49 + 16 * q^57 + 44 * q^60 - 24 * q^66 - 36 * q^68 + 72 * q^70 - 4 * q^72 - 20 * q^74 - 104 * q^76 - 40 * q^80 + 152 * q^81 + 64 * q^82 + 16 * q^84 + 48 * q^86 + 64 * q^88 - 40 * q^89 - 24 * q^92 + 48 * q^94 + 40 * q^96 + 8 * q^97 - 140 * 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.r.a	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	\(\Q(\sqrt{-1}) \)	None		✓			888.2.r.a	$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}-i q^{3}+2 i q^{4}+(-2 i-2)q^{5}+\cdots\)
888.2.r.b	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	\(\Q(\sqrt{-1}) \)	None		✓			888.2.r.b	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{2}+i q^{3}-2 i q^{4}+(2 i+2)q^{5}+\cdots\)
888.2.r.c	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	\(\Q(\sqrt{-1}) \)	None		✓			888.2.r.a	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{2}-i q^{3}+2 i q^{4}+(2 i+2)q^{5}+\cdots\)
888.2.r.d	$888$	$2$	888.r	296.j	$4$	$2$	$1$	$7.091$	\(\Q(\sqrt{-1}) \)	None		✓			888.2.r.b	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{2}+i q^{3}-2 i q^{4}+(-2 i-2)q^{5}+\cdots\)
888.2.r.e	$888$	$2$	888.r	296.j	$4$	$72$	$36$	$7.091$		None		✓			888.2.r.e	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
888.2.r.f	$888$	$2$	888.r	296.j	$4$	$72$	$36$	$7.091$		None		✓			888.2.r.f	$4$	$0$	\(6\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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