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

• Label: 847.2.v
• Level: $847$
• Weight: $2$
• Character orbit: 847.v
• Rep. character: $\chi_{847}(15,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $2640$
• Newform subspaces: $2$
• Sturm bound: $176$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.v (of order \(55\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{55})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(176\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	3600	2640	960
Cusp forms	3440	2640	800
Eisenstein series	160	0	160

Trace form

\( 2640 q + 4 q^{2} + 4 q^{3} + 68 q^{4} - 6 q^{6} + 2 q^{7} + 2 q^{8} - 654 q^{9} + O(q^{10}) \)

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.v.a	$847$	$2$	847.v	121.g	$55$	$1280$	$32$	$6.763$		None		$2$	$0$	\(1\)	\(25\)	\(-4\)	\(-32\)		$\mathrm{SU}(2)[C_{55}]$
847.2.v.b	$847$	$2$	847.v	121.g	$55$	$1360$	$34$	$6.763$		None		$2$	$0$	\(3\)	\(-21\)	\(4\)	\(34\)		$\mathrm{SU}(2)[C_{55}]$

Decomposition of \(S_{2}^{\mathrm{old}}(847, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(847, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)