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

• Label: 990.2.bv
• Level: $990$
• Weight: $2$
• Character orbit: 990.bv
• Rep. character: $\chi_{990}(47,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $1152$
• 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.bv (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 495 \)
Character field:			\(\Q(\zeta_{60})\)
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	3584	1152	2432
Cusp forms	3328	1152	2176
Eisenstein series	256	0	256

Trace form

1152 * q - 4 * q^3 + 24 * q^11 - 16 * q^12 - 4 * q^15 - 144 * q^16 + 12 * q^20 + 16 * q^21 + 12 * q^25 + 8 * q^27 + 92 * q^33 - 16 * q^36 + 24 * q^37 + 108 * q^38 - 64 * q^42 - 32 * q^45 + 12 * q^47 - 8 * q^48 - 96 * q^50 + 56 * q^51 + 48 * q^57 + 36 * q^58 + 4 * q^60 + 40 * q^63 + 8 * q^66 - 48 * q^67 - 92 * q^75 + 288 * q^77 + 16 * q^78 - 72 * q^81 - 120 * q^83 - 216 * q^86 + 128 * q^87 - 48 * q^90 + 144 * q^91 - 16 * q^93 + 12 * q^97

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.bv.a	$990$	$2$	990.bv	495.av	$60$	$1152$	$72$	$7.905$		None		✓	✓	✓	990.2.bv.a	$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{60}]$

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

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