Space of modular forms of level 891, weight 1, and Character 891.w

• Label: 891.1.w
• Level: $891$
• Weight: $1$
• Character orbit: 891.w
• Rep. character: $\chi_{891}(43,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	891.w (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 891 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(891, [\chi])\).

	Total	New	Old
Modular forms	54	54	0
Cusp forms	18	18	0
Eisenstein series	36	36	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	18	0	0	0

Trace form

\( 18 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(891, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
891.1.w.a	$891$	$1$	891.w	891.w	$54$	$18$	$1$	$0.445$	\(\Q(\zeta_{54})\)	$D_{27}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{6}+\zeta_{54}^{8}+\cdots)q^{5}+\cdots\)