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

• Label: 990.2.bn
• Level: $990$
• Weight: $2$
• Character orbit: 990.bn
• Rep. character: $\chi_{990}(49,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $576$
• Newform subspaces: $1$
• Sturm bound: $432$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bn (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 495 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(432\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	1792	576	1216
Cusp forms	1664	576	1088
Eisenstein series	128	0	128

Trace form

576 * q - 72 * q^4 + 2 * q^5 - 20 * q^9 - 4 * q^11 + 6 * q^15 + 72 * q^16 - 2 * q^20 + 8 * q^21 - 6 * q^25 + 8 * q^29 + 18 * q^30 + 12 * q^31 + 60 * q^35 + 16 * q^36 - 112 * q^39 - 32 * q^41 - 8 * q^44 + 36 * q^45 - 72 * q^49 - 16 * q^50 - 52 * q^51 - 72 * q^54 + 12 * q^55 - 40 * q^59 + 144 * q^64 + 12 * q^65 + 84 * q^66 + 8 * q^69 - 12 * q^70 + 56 * q^71 + 56 * q^74 - 28 * q^75 + 48 * q^79 - 4 * q^80 + 108 * q^81 - 24 * q^84 + 36 * q^86 - 240 * q^89 - 84 * q^90 - 72 * q^91 + 16 * q^95 + 56 * 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.bn.a	$990$	$2$	990.bn	495.al	$30$	$576$	$72$	$7.905$		None		✓	✓	✓	990.2.bn.a	$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$

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

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