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

• Label: 2888.1.u
• Level: $2888$
• Weight: $1$
• Character orbit: 2888.u
• Rep. character: $\chi_{2888}(99,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $42$
• Newform subspaces: $7$
• Sturm bound: $380$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.u (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(380\)
Trace bound:			\(22\)

Dimensions

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

	Total	New	Old
Modular forms	174	138	36
Cusp forms	54	42	12
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	42	0	0	0

Trace form

\( 42 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} + O(q^{10}) \)

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.u.a	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{5}q^{2}+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots\)
2888.1.u.b	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}-\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots\)
2888.1.u.c	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots\)
2888.1.u.d	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$12$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots\)
2888.1.u.e	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{3}+\cdots\)
2888.1.u.f	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{5}q^{2}+(\zeta_{18}+\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots\)
2888.1.u.g	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{2}+(1+\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2888, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2888, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)