Space of modular forms of level 896, weight 2, and Character 896.bt

• Label: 896.2.bt
• Level: $896$
• Weight: $2$
• Character orbit: 896.bt
• Rep. character: $\chi_{896}(3,\cdot)$
• Character field: $\Q(\zeta_{96})$
• Dimension: $4032$
• Newform subspaces: $1$
• Sturm bound: $256$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bt (of order \(96\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 896 \)
Character field:			\(\Q(\zeta_{96})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(256\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(896, [\chi])\).

	Total	New	Old
Modular forms	4160	4160	0
Cusp forms	4032	4032	0
Eisenstein series	128	128	0

Trace form

\( 4032 q - 16 q^{2} - 48 q^{3} - 16 q^{4} - 48 q^{5} - 32 q^{7} - 64 q^{8} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(896, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
896.2.bt.a	$896$	$2$	896.bt	896.at	$96$	$4032$	$126$	$7.155$		None		$4$	$0$	\(-16\)	\(-48\)	\(-48\)	\(-32\)		$\mathrm{SU}(2)[C_{96}]$