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

• Label: 891.1.q
• Level: $891$
• Weight: $1$
• Character orbit: 891.q
• Rep. character: $\chi_{891}(10,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• 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.q (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 297 \)
Character field:			\(\Q(\zeta_{18})\)
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	18	36
Cusp forms	18	6	12
Eisenstein series	36	12	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + 3 q^{5} - 6 q^{20} - 3 q^{25} - 3 q^{31} + 3 q^{44} + 3 q^{47} + 3 q^{59} - 3 q^{64} + 6 q^{67} - 3 q^{89} + 6 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
891.1.q.a	$891$	$1$	891.q	297.q	$18$	$6$	$1$	$0.445$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-11}) \)	None			✓	✓	297.1.q.a	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{5}+\zeta_{18}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(891, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(891, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)