Space of modular forms of level 1568, weight 1, and Character 1568.s

• Label: 1568.1.s
• Level: $1568$
• Weight: $1$
• Character orbit: 1568.s
• Rep. character: $\chi_{1568}(129,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1568.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1568, [\chi])\).

	Total	New	Old
Modular forms	72	8	64
Cusp forms	8	8	0
Eisenstein series	64	0	64

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1568, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1568.1.s.a	$1568$	$1$	1568.s	7.d	$6$	$8$	$4$	$0.783$	8.0.339738624.1	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{3}+\beta _{7})q^{5}+\beta _{4}q^{9}+(\beta _{1}-\beta _{5})q^{13}+\cdots\)