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

\( 8 q + 6 q^{9} + O(q^{10}) \)

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	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{20}^{7}-\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{9}+\cdots\)