Space of modular forms of level 990, weight 2, and Character 990.t

• Label: 990.2.t
• Level: $990$
• Weight: $2$
• Character orbit: 990.t
• Rep. character: $\chi_{990}(131,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $432$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(432\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(990, [\chi])\).

	Total	New	Old
Modular forms	448	96	352
Cusp forms	416	96	320
Eisenstein series	32	0	32

Trace form

96 * q - 4 * q^3 - 48 * q^4 + 20 * q^9 - 18 * q^11 + 8 * q^12 - 8 * q^15 - 48 * q^16 + 6 * q^22 + 72 * q^23 + 48 * q^25 - 16 * q^27 + 14 * q^33 + 12 * q^34 - 4 * q^36 - 12 * q^38 + 16 * q^42 - 4 * q^48 + 48 * q^49 - 108 * q^59 - 8 * q^60 + 96 * q^64 - 4 * q^66 - 12 * q^67 + 152 * q^69 + 4 * q^75 - 12 * q^77 + 64 * q^78 + 20 * q^81 + 24 * q^82 - 60 * q^86 + 6 * q^88 + 48 * q^91 - 72 * q^92 - 136 * q^93 + 12 * q^97 - 92 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(990, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
990.2.t.a	$990$	$2$	990.t	99.g	$6$	$48$	$24$	$7.905$		None		✓			990.2.t.a	$2$	$0$	\(-24\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
990.2.t.b	$990$	$2$	990.t	99.g	$6$	$48$	$24$	$7.905$		None		✓			990.2.t.a	$2$	$0$	\(24\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(990, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(990, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)