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

• Label: 990.2.s
• Level: $990$
• Weight: $2$
• Character orbit: 990.s
• Rep. character: $\chi_{990}(529,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $120$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(1\)
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	120	328
Cusp forms	416	120	296
Eisenstein series	32	0	32

Trace form

120 * q + 60 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^11 + 20 * q^14 + 34 * q^15 - 60 * q^16 - 2 * q^20 + 56 * q^21 - 4 * q^24 - 6 * q^25 + 48 * q^26 + 4 * q^29 - 32 * q^30 + 12 * q^31 - 24 * q^35 - 20 * q^41 - 8 * q^44 - 32 * q^45 + 24 * q^46 + 72 * q^49 + 8 * q^50 - 96 * q^51 - 4 * q^54 + 12 * q^55 - 20 * q^56 - 12 * q^59 + 32 * q^60 - 12 * q^61 - 120 * q^64 + 60 * q^65 + 76 * q^69 - 8 * q^71 - 44 * q^75 - 4 * q^80 + 72 * q^81 + 28 * q^84 + 24 * q^85 - 32 * q^86 - 24 * q^89 + 8 * q^90 + 12 * q^94 - 24 * q^95 + 4 * q^96 - 20 * 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.s.a	$990$	$2$	990.s	45.j	$6$	$4$	$2$	$7.905$	\(\Q(\zeta_{12})\)	None		✓			990.2.s.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
990.2.s.b	$990$	$2$	990.s	45.j	$6$	$8$	$4$	$7.905$	8.0.303595776.1	None		✓			990.2.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}+(\beta _{3}+2\beta _{5})q^{3}+(1+\beta _{4})q^{4}+\cdots\)
990.2.s.c	$990$	$2$	990.s	45.j	$6$	$52$	$26$	$7.905$		None		✓			990.2.s.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
990.2.s.d	$990$	$2$	990.s	45.j	$6$	$56$	$28$	$7.905$		None		✓	✓		990.2.s.d	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(990, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)