Space of modular forms of level 1166, weight 2, and Character 1166.c

• Label: 1166.2.c
• Level: $1166$
• Weight: $2$
• Character orbit: 1166.c
• Rep. character: $\chi_{1166}(529,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $3$
• Sturm bound: $324$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 1166 = 2 \cdot 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1166.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(324\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1166, [\chi])\).

	Total	New	Old
Modular forms	166	46	120
Cusp forms	158	46	112
Eisenstein series	8	0	8

Trace form

46 * q - 46 * q^4 - 54 * q^9 - 8 * q^10 - 2 * q^11 + 8 * q^13 + 24 * q^15 + 46 * q^16 + 24 * q^17 - 70 * q^25 + 24 * q^29 + 54 * q^36 + 16 * q^37 - 4 * q^38 + 8 * q^40 - 16 * q^42 - 24 * q^43 + 2 * q^44 - 24 * q^46 + 28 * q^47 + 62 * q^49 - 8 * q^52 + 2 * q^53 - 36 * q^54 - 44 * q^57 - 24 * q^60 + 4 * q^62 + 32 * q^63 - 46 * q^64 + 8 * q^66 - 24 * q^68 + 20 * q^69 - 56 * q^70 + 16 * q^77 + 4 * q^78 + 70 * q^81 - 40 * q^82 - 40 * q^89 + 72 * q^90 + 40 * q^91 + 56 * q^93 - 60 * q^97 - 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1166, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1166.2.c.a	$1166$	$2$	1166.c	53.b	$2$	$2$	$2$	$9.311$	\(\Q(\sqrt{-1}) \)	None		✓			1166.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}-i q^{5}+q^{6}+\cdots\)
1166.2.c.b	$1166$	$2$	1166.c	53.b	$2$	$22$	$22$	$9.311$		None		✓			1166.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1166.2.c.c	$1166$	$2$	1166.c	53.b	$2$	$22$	$22$	$9.311$		None		✓			1166.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1166, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1166, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(583, [\chi])\)\(^{\oplus 2}\)