Space of modular forms of level 784, weight 2, and Character 784.bh

• Label: 784.2.bh
• Level: $784$
• Weight: $2$
• Character orbit: 784.bh
• Rep. character: $\chi_{784}(29,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $1320$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bh (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 784 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).

	Total	New	Old
Modular forms	1368	1368	0
Cusp forms	1320	1320	0
Eisenstein series	48	48	0

Trace form

\( 1320 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 10 q^{6} - 22 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(784, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
784.2.bh.a	$784$	$2$	784.bh	784.ah	$28$	$1320$	$110$	$6.260$		None		$4$	$0$	\(-10\)	\(-10\)	\(-10\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$