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

• Label: 990.2.k
• Level: $990$
• Weight: $2$
• Character orbit: 990.k
• Rep. character: $\chi_{990}(287,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	464	40	424
Cusp forms	400	40	360
Eisenstein series	64	0	64

Trace form

\( 40 q - 8 q^{13} - 40 q^{16} - 64 q^{31} - 8 q^{37} + 8 q^{40} + 8 q^{52} + 8 q^{58} + 64 q^{61} - 32 q^{67} + 32 q^{70} + 8 q^{73} + 64 q^{76} + 24 q^{82} - 96 q^{85} + 104 q^{97}+O(q^{100}) \)

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.k.a	$990$	$2$	990.k	15.e	$4$	$8$	$4$	$7.905$	\(\Q(\zeta_{16})\)	None		✓			990.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-\zeta_{16}-2\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
990.2.k.b	$990$	$2$	990.k	15.e	$4$	$8$	$4$	$7.905$	\(\Q(\zeta_{16})\)	None		✓			990.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(\zeta_{16}+2\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
990.2.k.c	$990$	$2$	990.k	15.e	$4$	$12$	$6$	$7.905$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			990.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}-\beta _{2}q^{4}+\beta _{11}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
990.2.k.d	$990$	$2$	990.k	15.e	$4$	$12$	$6$	$7.905$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			990.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{2}-\beta _{2}q^{4}-\beta _{11}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(990, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)