Space of modular forms of level 1028, weight 1, and Character 1028.h

• Label: 1028.1.h
• Level: $1028$
• Weight: $1$
• Character orbit: 1028.h
• Rep. character: $\chi_{1028}(707,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $129$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1028 = 2^{2} \cdot 257 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1028.h (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1028 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(129\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1028, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1028, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1028.1.h.a	$1028$	$1$	1028.h	1028.h	$8$	$4$	$1$	$0.513$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+q^{8}+\cdots\)