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

• Label: 891.2.d
• Level: $891$
• Weight: $2$
• Character orbit: 891.d
• Rep. character: $\chi_{891}(890,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $3$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
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	120	52	68
Cusp forms	96	44	52
Eisenstein series	24	8	16

Trace form

\( 44 q + 44 q^{4} + O(q^{10}) \)

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.d.a	$891$	$2$	891.d	33.d	$2$	$4$	$4$	$7.115$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+4q^{16}+\cdots\)
891.2.d.b	$891$	$2$	891.d	33.d	$2$	$16$	$16$	$7.115$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(2-\beta _{3})q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)
891.2.d.c	$891$	$2$	891.d	33.d	$2$	$24$	$24$	$7.115$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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