Space of modular forms of level 2289, weight 1, and Character 2289.eq

• Label: 2289.1.eq
• Level: $2289$
• Weight: $1$
• Character orbit: 2289.eq
• Rep. character: $\chi_{2289}(47,\cdot)$
• Character field: $\Q(\zeta_{108})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $293$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2289 = 3 \cdot 7 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2289.eq (of order \(108\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2289 \)
Character field:			\(\Q(\zeta_{108})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(293\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2289, [\chi])\).

	Total	New	Old
Modular forms	180	180	0
Cusp forms	36	36	0
Eisenstein series	144	144	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	36	0	0	0

Trace form

\( 36 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2289, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2289.1.eq.a	$2289$	$1$	2289.eq	2289.dq	$108$	$36$	$1$	$1.142$	\(\Q(\zeta_{108})\)	$D_{108}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	2289.1.eq.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{108}^{7}q^{3}-\zeta_{108}^{51}q^{4}-\zeta_{108}^{20}q^{7}+\cdots\)