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

• Label: 891.2.g
• Level: $891$
• Weight: $2$
• Character orbit: 891.g
• Rep. character: $\chi_{891}(296,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $6$
• Sturm bound: $216$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(216\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	240	100	140
Cusp forms	192	92	100
Eisenstein series	48	8	40

Trace form

\( 92 q - 40 q^{4} + O(q^{10}) \)

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.g.a	$891$	$2$	891.g	99.g	$6$	$4$	$2$	$7.115$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+(2-2\beta _{2})q^{4}+\beta _{1}q^{5}+\beta _{3}q^{11}-4\beta _{2}q^{16}+\cdots\)
891.2.g.b	$891$	$2$	891.g	99.g	$6$	$8$	$4$	$7.115$	8.0.764411904.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(-1-\beta _{2}-\beta _{3}+2\beta _{5})q^{4}+\cdots\)
891.2.g.c	$891$	$2$	891.g	99.g	$6$	$8$	$4$	$7.115$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{2}q^{2}+(-1+\zeta_{24})q^{4}+\zeta_{24}^{5}q^{5}+\cdots\)
891.2.g.d	$891$	$2$	891.g	99.g	$6$	$8$	$4$	$7.115$	8.0.764411904.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(-1-\beta _{2}-\beta _{3}+2\beta _{5})q^{4}+\cdots\)
891.2.g.e	$891$	$2$	891.g	99.g	$6$	$16$	$8$	$7.115$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
891.2.g.f	$891$	$2$	891.g	99.g	$6$	$48$	$24$	$7.115$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(891, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)