Space of modular forms of level 704, weight 1, and Character 704.x

• Label: 704.1.x
• Level: $704$
• Weight: $1$
• Character orbit: 704.x
• Rep. character: $\chi_{704}(161,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$704 = 2^{6} \cdot 11$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	704.x (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$88$
Character field:			$\Q(\zeta_{10})$
Newform subspaces:			$1$
Sturm bound:			$96$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(704, [\chi])$.

	Total	New	Old
Modular forms	56	8	48
Cusp forms	8	8	0
Eisenstein series	48	0	48

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

$8 q + 6 q^{9} - 2 q^{25} - 6 q^{33} - 2 q^{49} - 10 q^{57} - 4 q^{89} + 6 q^{97}+O(q^{100})$

Decomposition of $S_{1}^{\mathrm{new}}(704, [\chi])$ 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
704.1.x.a	$704$	$1$	704.x	88.p	$10$	$8$	$2$	$0.351$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-2})$	None		✓	✓	✓	704.1.x.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{20}^{7}-\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{9}+\cdots$