Space of modular forms of level 567, weight 1, and Character 567.k

• Label: 567.1.k
• Level: $567$
• Weight: $1$
• Character orbit: 567.k
• Rep. character: $\chi_{567}(460,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	567.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(567, [\chi])\).

	Total	New	Old
Modular forms	26	6	20
Cusp forms	2	2	0
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + q^{4} + q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
567.1.k.a	$567$	$1$	567.k	63.k	$6$	$2$	$1$	$0.283$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None			189.1.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}+(-1+\zeta_{6}^{2})q^{13}+\cdots\)