Space of modular forms of level 688, weight 2, and Character 688.bh

• Label: 688.2.bh
• Level: $688$
• Weight: $2$
• Character orbit: 688.bh
• Rep. character: $\chi_{688}(21,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $1032$
• Newform subspaces: $1$
• Sturm bound: $176$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 688 = 2^{4} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	688.bh (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 688 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(176\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(688, [\chi])\).

	Total	New	Old
Modular forms	1080	1080	0
Cusp forms	1032	1032	0
Eisenstein series	48	48	0

Trace form

\( 1032 q - 10 q^{2} - 10 q^{3} - 14 q^{4} - 10 q^{5} - 24 q^{6} - 10 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(688, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
688.2.bh.a	$688$	$2$	688.bh	688.ah	$28$	$1032$	$86$	$5.494$		None		$4$	$0$	\(-10\)	\(-10\)	\(-10\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$