Space of modular forms of level 990 and weight 3

• Label: 990.3
• Level: 990
• Weight: 3
• Dimension: 12336
• Nonzero newspaces: 24
• Sturm bound: 155520
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(155520\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(990))\).

	Total	New	Old
Modular forms	53120	12336	40784
Cusp forms	50560	12336	38224
Eisenstein series	2560	0	2560

Trace form

12336 * q + 4 * q^2 - 36 * q^5 - 48 * q^6 + 28 * q^7 - 8 * q^8 - 32 * q^9 - 84 * q^10 - 64 * q^11 + 16 * q^12 - 112 * q^13 + 64 * q^14 + 84 * q^15 + 16 * q^16 + 200 * q^17 + 32 * q^18 + 92 * q^19 + 80 * q^20 - 72 * q^21 - 8 * q^22 - 596 * q^23 - 160 * q^24 - 620 * q^25 - 696 * q^26 - 696 * q^27 - 128 * q^28 - 628 * q^29 + 24 * q^30 + 104 * q^31 - 16 * q^32 + 580 * q^33 + 320 * q^34 + 1498 * q^35 + 384 * q^36 + 692 * q^37 + 1160 * q^38 + 1552 * q^39 + 168 * q^40 + 1764 * q^41 + 864 * q^42 + 480 * q^43 + 160 * q^44 - 8 * q^45 - 48 * q^46 - 836 * q^47 - 32 * q^48 - 932 * q^49 - 724 * q^50 - 1720 * q^51 - 24 * q^52 - 2624 * q^53 - 816 * q^54 - 164 * q^55 + 64 * q^56 - 2016 * q^57 + 432 * q^58 - 1176 * q^59 - 296 * q^60 - 444 * q^61 - 344 * q^62 - 120 * q^63 - 192 * q^64 + 504 * q^65 - 528 * q^66 + 628 * q^67 + 208 * q^68 + 312 * q^69 - 84 * q^70 + 1760 * q^71 - 384 * q^72 + 712 * q^73 + 368 * q^74 + 2204 * q^75 + 192 * q^76 + 3640 * q^77 + 896 * q^78 + 788 * q^79 - 40 * q^80 + 5136 * q^81 - 640 * q^82 + 3732 * q^83 + 2144 * q^84 + 110 * q^85 + 2880 * q^86 + 4728 * q^87 - 224 * q^88 + 2140 * q^89 + 1472 * q^90 - 1796 * q^91 + 1048 * q^92 + 1192 * q^93 - 584 * q^94 - 2334 * q^95 + 64 * q^96 + 188 * q^97 - 988 * q^98 - 1508 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(990))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
990.3.b	\(\chi_{990}(901, \cdot)\)	990.3.b.a	8	1
		990.3.b.b	8
		990.3.b.c	8
		990.3.b.d	16
990.3.e	\(\chi_{990}(89, \cdot)\)	990.3.e.a	40	1
990.3.g	\(\chi_{990}(881, \cdot)\)	990.3.g.a	16	1
		990.3.g.b	16
990.3.h	\(\chi_{990}(109, \cdot)\)	990.3.h.a	4	1
		990.3.h.b	8
		990.3.h.c	24
		990.3.h.d	24
990.3.j	\(\chi_{990}(397, \cdot)\)	990.3.j.a	8	2
		990.3.j.b	12
		990.3.j.c	16
		990.3.j.d	20
		990.3.j.e	20
		990.3.j.f	24
990.3.l	\(\chi_{990}(197, \cdot)\)	990.3.l.a	4	2
		990.3.l.b	4
		990.3.l.c	44
		990.3.l.d	44
990.3.p	\(\chi_{990}(221, \cdot)\)	n/a	160	2
990.3.q	\(\chi_{990}(439, \cdot)\)	n/a	288	2
990.3.r	\(\chi_{990}(241, \cdot)\)	n/a	192	2
990.3.u	\(\chi_{990}(419, \cdot)\)	n/a	240	2
990.3.v	\(\chi_{990}(19, \cdot)\)	n/a	240	4
990.3.w	\(\chi_{990}(71, \cdot)\)	n/a	128	4
990.3.y	\(\chi_{990}(179, \cdot)\)	n/a	192	4
990.3.bb	\(\chi_{990}(271, \cdot)\)	n/a	160	4
990.3.bd	\(\chi_{990}(67, \cdot)\)	n/a	480	4
990.3.bf	\(\chi_{990}(263, \cdot)\)	n/a	576	4
990.3.bi	\(\chi_{990}(17, \cdot)\)	n/a	384	8
990.3.bk	\(\chi_{990}(37, \cdot)\)	n/a	480	8
990.3.bl	\(\chi_{990}(59, \cdot)\)	n/a	1152	8
990.3.bo	\(\chi_{990}(61, \cdot)\)	n/a	768	8
990.3.bp	\(\chi_{990}(79, \cdot)\)	n/a	1152	8
990.3.bq	\(\chi_{990}(191, \cdot)\)	n/a	768	8
990.3.bs	\(\chi_{990}(83, \cdot)\)	n/a	2304	16
990.3.bu	\(\chi_{990}(97, \cdot)\)	n/a	2304	16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(990))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(990)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)