Space of modular forms of level 891, weight 2, and Character 891.bd

• Label: 891.2.bd
• Level: $891$
• Weight: $2$
• Character orbit: 891.bd
• Rep. character: $\chi_{891}(2,\cdot)$
• Character field: $\Q(\zeta_{270})$
• Dimension: $7632$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.bd (of order \(270\) and degree \(72\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 891 \)
Character field:			\(\Q(\zeta_{270})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(891, [\chi])\).

	Total	New	Old
Modular forms	7920	7920	0
Cusp forms	7632	7632	0
Eisenstein series	288	288	0

Trace form

\( 7632 q - 90 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 90 q^{6} - 90 q^{7} - 90 q^{8} - 54 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(891, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
891.2.bd.a	$891$	$2$	891.bd	891.ad	$270$	$7632$	$106$	$7.115$		None		$4$	$0$	\(-90\)	\(-54\)	\(-54\)	\(-90\)		$\mathrm{SU}(2)[C_{270}]$