Space of modular forms of level 2888, weight 1, and Character 2888.s

• Label: 2888.1.s
• Level: $2888$
• Weight: $1$
• Character orbit: 2888.s
• Rep. character: $\chi_{2888}(333,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $380$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.s (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(380\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2888, [\chi])\).

	Total	New	Old
Modular forms	132	108	24
Cusp forms	12	12	0
Eisenstein series	120	96	24

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

\( 12 q + 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2888, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2888.1.s.a	$2888$	$1$	2888.s	152.s	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots\)
2888.1.s.b	$2888$	$1$	2888.s	152.s	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q+\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots\)