Space of modular forms of level 704, weight 2, and Character 704.bb

• Label: 704.2.bb
• Level: $704$
• Weight: $2$
• Character orbit: 704.bb
• Rep. character: $\chi_{704}(43,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $752$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.bb (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 704 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(704, [\chi])\).

	Total	New	Old
Modular forms	784	784	0
Cusp forms	752	752	0
Eisenstein series	32	32	0

Trace form

752 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 8 * q^11 - 16 * q^12 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^20 - 16 * q^22 - 16 * q^23 - 16 * q^25 - 96 * q^26 - 16 * q^27 - 32 * q^31 + 64 * q^34 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^42 - 16 * q^44 - 16 * q^45 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 16 * q^53 + 56 * q^55 + 96 * q^56 - 16 * q^58 + 48 * q^59 - 112 * q^60 + 176 * q^64 - 120 * q^66 - 176 * q^67 - 16 * q^69 - 112 * q^70 + 48 * q^71 - 144 * q^75 - 8 * q^77 + 80 * q^78 - 144 * q^80 - 16 * q^81 - 16 * q^82 - 224 * q^86 + 72 * q^88 - 16 * q^89 - 16 * q^91 + 288 * q^92 - 64 * q^93 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(704, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
704.2.bb.a	$704$	$2$	704.bb	704.ab	$16$	$752$	$94$	$5.621$		None		✓	✓	✓	704.2.bb.a	$4$	$0$	\(0\)	\(-16\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$