Space of modular forms of level 888, weight 1, and Character 888.i

• Label: 888.1.i
• Level: $888$
• Weight: $1$
• Character orbit: 888.i
• Rep. character: $\chi_{888}(221,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	888.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 888 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(152\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(888, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	12	12	0
Eisenstein series	4	4	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

12 * q + 4 * q^4 - 4 * q^7 - 4 * q^9 + 4 * q^16 - 4 * q^25 - 12 * q^28 - 8 * q^30 - 4 * q^33 + 4 * q^34 + 4 * q^36 + 8 * q^40 - 4 * q^46 + 8 * q^48 + 8 * q^49 + 8 * q^58 - 4 * q^63 + 4 * q^64 - 8 * q^70 - 4 * q^73 - 4 * q^78 + 12 * q^81 - 8 * q^84

Decomposition of \(S_{1}^{\mathrm{new}}(888, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
888.1.i.a	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓	✓			888.1.i.a	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
888.1.i.b	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓	✓			888.1.i.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
888.1.i.c	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓	✓			888.1.i.a	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
888.1.i.d	$888$	$1$	888.i	888.i	$2$	$1$	$1$	$0.443$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-222}) \)	None	✓	✓			888.1.i.a	$2$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
888.1.i.e	$888$	$1$	888.i	888.i	$2$	$8$	$8$	$0.443$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-111}) \)	None		✓	✓		888.1.i.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{16}q^{2}-\zeta_{16}^{4}q^{3}+\zeta_{16}^{2}q^{4}+(\zeta_{16}^{3}+\cdots)q^{5}+\cdots\)