Space of modular forms of level 833, weight 2, and Character 833.bg

• Label: 833.2.bg
• Level: $833$
• Weight: $2$
• Character orbit: 833.bg
• Rep. character: $\chi_{833}(4,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $1968$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.bg (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 833 \)
Character field:			\(\Q(\zeta_{84})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(833, [\chi])\).

	Total	New	Old
Modular forms	2064	2064	0
Cusp forms	1968	1968	0
Eisenstein series	96	96	0

Trace form

\( 1968 q - 26 q^{3} - 212 q^{4} - 24 q^{5} - 12 q^{6} - 22 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(833, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
833.2.bg.a	$833$	$2$	833.bg	833.ag	$84$	$1968$	$82$	$6.652$		None		$4$	$0$	\(0\)	\(-26\)	\(-24\)	\(-22\)		$\mathrm{SU}(2)[C_{84}]$