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

• Label: 891.2.y
• Level: $891$
• Weight: $2$
• Character orbit: 891.y
• Rep. character: $\chi_{891}(32,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $1908$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.y (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 891 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	1980	1980	0
Cusp forms	1908	1908	0
Eisenstein series	72	72	0

Trace form

\( 1908 q - 36 q^{3} - 36 q^{4} - 36 q^{5} - 36 q^{9} + O(q^{10}) \)

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.y.a	$891$	$2$	891.y	891.y	$54$	$36$	$2$	$7.115$		\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{54}]$
891.2.y.b	$891$	$2$	891.y	891.y	$54$	$1872$	$104$	$7.115$		None		$4$	$0$	\(0\)	\(-36\)	\(-36\)	\(0\)		$\mathrm{SU}(2)[C_{54}]$