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

• Label: 990.2.n
• Level: $990$
• Weight: $2$
• Character orbit: 990.n
• Rep. character: $\chi_{990}(91,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $80$
• Newform subspaces: $13$
• Sturm bound: $432$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(432\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	928	80	848
Cusp forms	800	80	720
Eisenstein series	128	0	128

Trace form

80 * q - 2 * q^2 - 20 * q^4 - 2 * q^8 - 8 * q^10 - 20 * q^11 - 8 * q^13 + 2 * q^14 - 20 * q^16 - 16 * q^17 - 14 * q^19 + 10 * q^22 - 32 * q^23 - 20 * q^25 + 32 * q^26 + 16 * q^29 + 28 * q^31 + 8 * q^32 + 36 * q^34 + 16 * q^37 + 8 * q^38 + 2 * q^40 + 34 * q^41 - 20 * q^43 + 10 * q^44 + 16 * q^46 - 24 * q^47 - 34 * q^49 - 2 * q^50 + 12 * q^52 + 48 * q^53 + 8 * q^55 + 12 * q^56 - 20 * q^58 - 14 * q^59 + 40 * q^61 - 28 * q^62 - 20 * q^64 + 28 * q^65 - 12 * q^67 - 16 * q^68 + 68 * q^71 - 8 * q^73 - 36 * q^74 + 16 * q^76 - 80 * q^77 - 8 * q^79 - 66 * q^82 + 26 * q^83 + 28 * q^85 + 2 * q^86 - 10 * q^88 - 40 * q^89 - 62 * q^91 + 48 * q^92 - 18 * q^94 - 42 * q^97 + 40 * q^98

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.n.a	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None					330.2.m.d	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
990.2.n.b	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None		✓			990.2.n.b	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
990.2.n.c	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None					110.2.g.b	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
990.2.n.d	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None					330.2.m.c	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
990.2.n.e	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None					330.2.m.b	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
990.2.n.f	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None					110.2.g.a	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
990.2.n.g	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None		✓			990.2.n.b	$2$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
990.2.n.h	$990$	$2$	990.n	11.c	$5$	$4$	$1$	$7.905$	\(\Q(\zeta_{10})\)	None					330.2.m.a	$2$	$0$	\(1\)	\(0\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
990.2.n.i	$990$	$2$	990.n	11.c	$5$	$8$	$2$	$7.905$	8.0.2769390625.1	None					330.2.m.f	$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{4}+\cdots\)
990.2.n.j	$990$	$2$	990.n	11.c	$5$	$8$	$2$	$7.905$	8.0.682515625.5	None					110.2.g.c	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{2}-\beta _{2}q^{4}+\cdots\)
990.2.n.k	$990$	$2$	990.n	11.c	$5$	$8$	$2$	$7.905$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					330.2.m.e	$2$	$0$	\(2\)	\(0\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{2}q^{2}-\beta _{3}q^{4}+(1-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
990.2.n.l	$990$	$2$	990.n	11.c	$5$	$12$	$3$	$7.905$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			990.2.n.l	$2$	$0$	\(-3\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{3}q^{2}-\beta _{4}q^{4}-\beta _{2}q^{5}-\beta _{6}q^{7}+\cdots\)
990.2.n.m	$990$	$2$	990.n	11.c	$5$	$12$	$3$	$7.905$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			990.2.n.l	$2$	$0$	\(3\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{4}+\beta _{2}q^{5}-\beta _{6}q^{7}+\cdots\)

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

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