Space of modular forms of level 2163, weight 1, and Character 2163.cz

• Label: 2163.1.cz
• Level: $2163$
• Weight: $1$
• Character orbit: 2163.cz
• Rep. character: $\chi_{2163}(2,\cdot)$
• Character field: $\Q(\zeta_{102})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $277$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2163 = 3 \cdot 7 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2163.cz (of order \(102\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2163 \)
Character field:			\(\Q(\zeta_{102})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(277\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2163, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	32	32	0
Eisenstein series	128	128	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q + q^{3} - 2 q^{4} - 2 q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2163, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2163.1.cz.a	$2163$	$1$	2163.cz	2163.bz	$102$	$32$	$1$	$1.079$	\(\Q(\zeta_{51})\)	$D_{51}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	2163.1.cn.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{102}^{40}q^{3}+\zeta_{102}^{24}q^{4}-\zeta_{102}^{9}q^{7}+\cdots\)