Space of modular forms of level 847, weight 2, and Character 847.bc

• Label: 847.2.bc
• Level: $847$
• Weight: $2$
• Character orbit: 847.bc
• Rep. character: $\chi_{847}(4,\cdot)$
• Character field: $\Q(\zeta_{165})$
• Dimension: $6880$
• Newform subspaces: $1$
• Sturm bound: $176$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.bc (of order \(165\) and degree \(80\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 847 \)
Character field:			\(\Q(\zeta_{165})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(176\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(847, [\chi])\).

	Total	New	Old
Modular forms	7200	7200	0
Cusp forms	6880	6880	0
Eisenstein series	320	320	0

Trace form

\( 6880 q - 39 q^{2} - 30 q^{3} - 123 q^{4} - 43 q^{5} - 208 q^{6} - 81 q^{7} - 148 q^{8} + 784 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
847.2.bc.a	$847$	$2$	847.bc	847.ac	$165$	$6880$	$86$	$6.763$		None		$4$	$0$	\(-39\)	\(-30\)	\(-43\)	\(-81\)		$\mathrm{SU}(2)[C_{165}]$