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

• Label: 891.2.bb
• Level: $891$
• Weight: $2$
• Character orbit: 891.bb
• Rep. character: $\chi_{891}(8,\cdot)$
• Character field: $\Q(\zeta_{90})$
• Dimension: $816$
• 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.bb (of order \(90\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 297 \)
Character field:			\(\Q(\zeta_{90})\)
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	2736	912	1824
Cusp forms	2448	816	1632
Eisenstein series	288	96	192

Trace form

\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + O(q^{10}) \)

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.bb.a	$891$	$2$	891.bb	297.x	$90$	$816$	$34$	$7.115$		None		$4$	$0$	\(30\)	\(0\)	\(21\)	\(-30\)		$\mathrm{SU}(2)[C_{90}]$

Decomposition of \(S_{2}^{\mathrm{old}}(891, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(891, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)