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

• Label: 891.2.f
• Level: $891$
• Weight: $2$
• Character orbit: 891.f
• Rep. character: $\chi_{891}(82,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $176$
• Newform subspaces: $7$
• Sturm bound: $216$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(216\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	480	208	272
Cusp forms	384	176	208
Eisenstein series	96	32	64

Trace form

176 * q - 34 * q^4 + 6 * q^7 - 40 * q^10 + 6 * q^13 - 10 * q^16 + 6 * q^19 + 22 * q^22 - 28 * q^25 - 72 * q^28 - 4 * q^34 - 18 * q^37 + 26 * q^40 + 28 * q^43 + 24 * q^46 - 50 * q^49 + 30 * q^52 - 26 * q^55 + 82 * q^58 + 6 * q^61 + 16 * q^64 + 76 * q^67 + 56 * q^70 - 24 * q^73 - 20 * q^76 - 114 * q^79 - 2 * q^82 - 74 * q^85 - 2 * q^88 + 44 * q^91 - 98 * q^94 + 18 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
891.2.f.a	$891$	$2$	891.f	11.c	$5$	$4$	$1$	$7.115$	\(\Q(\zeta_{10})\)	None					99.2.m.a	$2$	$0$	\(-4\)	\(0\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
891.2.f.b	$891$	$2$	891.f	11.c	$5$	$4$	$1$	$7.115$	\(\Q(\zeta_{10})\)	None					99.2.m.a	$2$	$0$	\(4\)	\(0\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots\)
891.2.f.c	$891$	$2$	891.f	11.c	$5$	$24$	$6$	$7.115$		None		✓			891.2.f.c	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(7\)		$\mathrm{SU}(2)[C_{5}]$
891.2.f.d	$891$	$2$	891.f	11.c	$5$	$24$	$6$	$7.115$		None		✓			891.2.f.c	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(7\)		$\mathrm{SU}(2)[C_{5}]$
891.2.f.e	$891$	$2$	891.f	11.c	$5$	$36$	$9$	$7.115$		None					99.2.m.b	$2$	$0$	\(-1\)	\(0\)	\(-8\)	\(2\)		$\mathrm{SU}(2)[C_{5}]$
891.2.f.f	$891$	$2$	891.f	11.c	$5$	$36$	$9$	$7.115$		None					99.2.m.b	$2$	$0$	\(1\)	\(0\)	\(8\)	\(2\)		$\mathrm{SU}(2)[C_{5}]$
891.2.f.g	$891$	$2$	891.f	11.c	$5$	$48$	$12$	$7.115$		None		✓	✓		891.2.f.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-14\)		$\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(891, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)