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

• Label: 990.2.ba
• Level: $990$
• Weight: $2$
• Character orbit: 990.ba
• Rep. character: $\chi_{990}(289,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $120$
• Newform subspaces: $9$
• Sturm bound: $432$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.ba (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(432\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(13\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	928	120	808
Cusp forms	800	120	680
Eisenstein series	128	0	128

Trace form

120 * q + 30 * q^4 - 6 * q^5 + 4 * q^10 + 6 * q^11 - 6 * q^14 - 30 * q^16 + 16 * q^19 + 6 * q^20 - 14 * q^25 - 4 * q^26 + 4 * q^29 + 32 * q^31 - 8 * q^34 + 8 * q^35 + 6 * q^40 + 14 * q^41 + 14 * q^44 - 24 * q^46 + 28 * q^49 + 28 * q^50 - 36 * q^55 - 4 * q^56 + 80 * q^59 - 56 * q^61 + 30 * q^64 + 20 * q^65 + 36 * q^70 - 4 * q^71 + 8 * q^74 - 36 * q^76 + 4 * q^79 + 4 * q^80 + 42 * q^85 - 80 * q^86 + 132 * q^89 + 2 * q^91 - 22 * q^94 + 110 * q^95

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.ba.a	$990$	$2$	990.ba	55.j	$10$	$8$	$2$	$7.905$	\(\Q(\zeta_{20})\)	None					330.2.s.b	$4$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+(-2+\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
990.2.ba.b	$990$	$2$	990.ba	55.j	$10$	$8$	$2$	$7.905$	\(\Q(\zeta_{20})\)	None					110.2.j.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\cdots\)
990.2.ba.c	$990$	$2$	990.ba	55.j	$10$	$8$	$2$	$7.905$	\(\Q(\zeta_{20})\)	None		✓			990.2.ba.c	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\cdots\)
990.2.ba.d	$990$	$2$	990.ba	55.j	$10$	$8$	$2$	$7.905$	\(\Q(\zeta_{20})\)	None					330.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\cdots\)
990.2.ba.e	$990$	$2$	990.ba	55.j	$10$	$8$	$2$	$7.905$	\(\Q(\zeta_{20})\)	None		✓			990.2.ba.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\zeta_{20}-\zeta_{20}^{3}+\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\cdots\)
990.2.ba.f	$990$	$2$	990.ba	55.j	$10$	$16$	$4$	$7.905$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			990.2.ba.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{12}q^{2}-\beta _{4}q^{4}+(\beta _{8}+2\beta _{9}+2\beta _{11}+\cdots)q^{5}+\cdots\)
990.2.ba.g	$990$	$2$	990.ba	55.j	$10$	$16$	$4$	$7.905$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			990.2.ba.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{12}q^{2}-\beta _{4}q^{4}+(-2\beta _{8}-\beta _{9}-2\beta _{12}+\cdots)q^{5}+\cdots\)
990.2.ba.h	$990$	$2$	990.ba	55.j	$10$	$16$	$4$	$7.905$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					110.2.j.b	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{5}q^{2}-\beta _{11}q^{4}+(\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
990.2.ba.i	$990$	$2$	990.ba	55.j	$10$	$32$	$8$	$7.905$		None			✓		330.2.s.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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