Space of modular forms of level 990, weight 3, and Character 990.b

• Label: 990.3.b
• Level: $990$
• Weight: $3$
• Character orbit: 990.b
• Rep. character: $\chi_{990}(901,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $648$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	990.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(648\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(990, [\chi])\).

	Total	New	Old
Modular forms	448	40	408
Cusp forms	416	40	376
Eisenstein series	32	0	32

Trace form

40 * q - 80 * q^4 - 32 * q^14 + 160 * q^16 + 8 * q^23 + 200 * q^25 - 112 * q^26 - 128 * q^31 + 80 * q^34 + 48 * q^37 + 96 * q^38 - 280 * q^47 - 296 * q^49 - 32 * q^53 + 64 * q^56 + 160 * q^58 - 208 * q^59 - 320 * q^64 + 24 * q^67 + 320 * q^71 + 184 * q^77 - 176 * q^82 + 128 * q^86 + 16 * q^89 + 624 * q^91 - 16 * q^92 - 640 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(990, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
990.3.b.a	$990$	$3$	990.b	11.b	$2$	$8$	$8$	$26.976$	8.0.\(\cdots\).3	None		✓			990.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-2q^{4}+\beta _{5}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
990.3.b.b	$990$	$3$	990.b	11.b	$2$	$8$	$8$	$26.976$	8.0.4956160000.2	None					110.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}+\beta _{1}q^{5}+(2\beta _{2}-2\beta _{5}+\cdots)q^{7}+\cdots\)
990.3.b.c	$990$	$3$	990.b	11.b	$2$	$8$	$8$	$26.976$	8.0.\(\cdots\).3	None		✓			990.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-2q^{4}-\beta _{5}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
990.3.b.d	$990$	$3$	990.b	11.b	$2$	$16$	$16$	$26.976$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None			✓		330.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}-\beta _{5}q^{5}+(2\beta _{1}+\beta _{10}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(990, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(990, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)