Space of modular forms of level 9633 and weight 2

• Label: 9633.2
• Level: 9633
• Weight: 2
• Dimension: 2504146
• Nonzero newspaces: 96
• Sturm bound: 13628160

Defining parameters

Level:	\( N \)	=	\( 9633 = 3 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 96 \)
Sturm bound:			\(13628160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9633))\).

	Total	New	Old
Modular forms	3423456	2518054	905402
Cusp forms	3390625	2504146	886479
Eisenstein series	32831	13908	18923

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9633))\)

We only show spaces with even 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
9633.2.a	\(\chi_{9633}(1, \cdot)\)	9633.2.a.a	1	1
		9633.2.a.b	1
		9633.2.a.c	1
		9633.2.a.d	1
		9633.2.a.e	1
		9633.2.a.f	1
		9633.2.a.g	1
		9633.2.a.h	1
		9633.2.a.i	1
		9633.2.a.j	1
		9633.2.a.k	1
		9633.2.a.l	1
		9633.2.a.m	1
		9633.2.a.n	1
		9633.2.a.o	1
		9633.2.a.p	1
		9633.2.a.q	1
		9633.2.a.r	1
		9633.2.a.s	2
		9633.2.a.t	2
		9633.2.a.u	3
		9633.2.a.v	4
		9633.2.a.w	5
		9633.2.a.x	5
		9633.2.a.y	6
		9633.2.a.z	6
		9633.2.a.ba	9
		9633.2.a.bb	9
		9633.2.a.bc	9
		9633.2.a.bd	10
		9633.2.a.be	10
		9633.2.a.bf	10
		9633.2.a.bg	10
		9633.2.a.bh	11
		9633.2.a.bi	11
		9633.2.a.bj	11
		9633.2.a.bk	11
		9633.2.a.bl	18
		9633.2.a.bm	18
		9633.2.a.bn	22
		9633.2.a.bo	22
		9633.2.a.bp	22
		9633.2.a.bq	22
		9633.2.a.br	24
		9633.2.a.bs	24
		9633.2.a.bt	30
		9633.2.a.bu	30
		9633.2.a.bv	36
		9633.2.a.bw	36
9633.2.b	\(\chi_{9633}(9463, \cdot)\)	n/a	460	1
9633.2.d	\(\chi_{9633}(9632, \cdot)\)	n/a	1008	1
9633.2.g	\(\chi_{9633}(170, \cdot)\)	n/a	1012	1
9633.2.i	\(\chi_{9633}(2557, \cdot)\)	n/a	1028	2
9633.2.j	\(\chi_{9633}(5578, \cdot)\)	n/a	1032	2
9633.2.k	\(\chi_{9633}(6613, \cdot)\)	n/a	928	2
9633.2.l	\(\chi_{9633}(3526, \cdot)\)	n/a	1028	2
9633.2.m	\(\chi_{9633}(1958, \cdot)\)	n/a	1848	2
9633.2.o	\(\chi_{9633}(5338, \cdot)\)	n/a	1024	2
9633.2.r	\(\chi_{9633}(3527, \cdot)\)	n/a	2012	2
9633.2.t	\(\chi_{9633}(2344, \cdot)\)	n/a	1028	2
9633.2.u	\(\chi_{9633}(6782, \cdot)\)	n/a	2012	2
9633.2.z	\(\chi_{9633}(1205, \cdot)\)	n/a	2012	2
9633.2.bb	\(\chi_{9633}(677, \cdot)\)	n/a	2024	2
9633.2.be	\(\chi_{9633}(1882, \cdot)\)	n/a	920	2
9633.2.bf	\(\chi_{9633}(506, \cdot)\)	n/a	2016	2
9633.2.bh	\(\chi_{9633}(2558, \cdot)\)	n/a	2012	2
9633.2.bj	\(\chi_{9633}(5407, \cdot)\)	n/a	1024	2
9633.2.bl	\(\chi_{9633}(1375, \cdot)\)	n/a	1028	2
9633.2.bo	\(\chi_{9633}(2051, \cdot)\)	n/a	2012	2
9633.2.bq	\(\chi_{9633}(2174, \cdot)\)	n/a	2012	2
9633.2.bs	\(\chi_{9633}(484, \cdot)\)	n/a	3078	6
9633.2.bt	\(\chi_{9633}(2536, \cdot)\)	n/a	3102	6
9633.2.bu	\(\chi_{9633}(1498, \cdot)\)	n/a	3078	6
9633.2.bw	\(\chi_{9633}(2953, \cdot)\)	n/a	2056	4
9633.2.by	\(\chi_{9633}(995, \cdot)\)	n/a	4024	4
9633.2.ca	\(\chi_{9633}(596, \cdot)\)	n/a	4024	4
9633.2.cb	\(\chi_{9633}(4483, \cdot)\)	n/a	2056	4
9633.2.cd	\(\chi_{9633}(2098, \cdot)\)	n/a	2048	4
9633.2.cf	\(\chi_{9633}(1103, \cdot)\)	n/a	3696	4
9633.2.ch	\(\chi_{9633}(239, \cdot)\)	n/a	4032	4
9633.2.ck	\(\chi_{9633}(2554, \cdot)\)	n/a	2056	4
9633.2.cl	\(\chi_{9633}(742, \cdot)\)	n/a	6528	12
9633.2.co	\(\chi_{9633}(823, \cdot)\)	n/a	3078	6
9633.2.cp	\(\chi_{9633}(485, \cdot)\)	n/a	6042	6
9633.2.cq	\(\chi_{9633}(2198, \cdot)\)	n/a	6066	6
9633.2.cr	\(\chi_{9633}(146, \cdot)\)	n/a	6042	6
9633.2.da	\(\chi_{9633}(4079, \cdot)\)	n/a	6042	6
9633.2.db	\(\chi_{9633}(2027, \cdot)\)	n/a	6036	6
9633.2.dc	\(\chi_{9633}(2365, \cdot)\)	n/a	3084	6
9633.2.dd	\(\chi_{9633}(4417, \cdot)\)	n/a	3078	6
9633.2.de	\(\chi_{9633}(1667, \cdot)\)	n/a	6042	6
9633.2.di	\(\chi_{9633}(911, \cdot)\)	n/a	14496	12
9633.2.dl	\(\chi_{9633}(740, \cdot)\)	n/a	14496	12
9633.2.dn	\(\chi_{9633}(571, \cdot)\)	n/a	6576	12
9633.2.do	\(\chi_{9633}(587, \cdot)\)	n/a	12084	12
9633.2.dp	\(\chi_{9633}(319, \cdot)\)	n/a	6156	12
9633.2.du	\(\chi_{9633}(925, \cdot)\)	n/a	6156	12
9633.2.dv	\(\chi_{9633}(80, \cdot)\)	n/a	12084	12
9633.2.dy	\(\chi_{9633}(70, \cdot)\)	n/a	6168	12
9633.2.dz	\(\chi_{9633}(746, \cdot)\)	n/a	12072	12
9633.2.ea	\(\chi_{9633}(178, \cdot)\)	n/a	14544	24
9633.2.eb	\(\chi_{9633}(172, \cdot)\)	n/a	13056	24
9633.2.ec	\(\chi_{9633}(235, \cdot)\)	n/a	14592	24
9633.2.ed	\(\chi_{9633}(334, \cdot)\)	n/a	14544	24
9633.2.ef	\(\chi_{9633}(151, \cdot)\)	n/a	14592	24
9633.2.eh	\(\chi_{9633}(476, \cdot)\)	n/a	26208	24
9633.2.ej	\(\chi_{9633}(620, \cdot)\)	n/a	29040	24
9633.2.el	\(\chi_{9633}(56, \cdot)\)	n/a	29040	24
9633.2.eo	\(\chi_{9633}(277, \cdot)\)	n/a	14544	24
9633.2.eq	\(\chi_{9633}(64, \cdot)\)	n/a	14592	24
9633.2.es	\(\chi_{9633}(335, \cdot)\)	n/a	29040	24
9633.2.eu	\(\chi_{9633}(350, \cdot)\)	n/a	28992	24
9633.2.ev	\(\chi_{9633}(400, \cdot)\)	n/a	13152	24
9633.2.ey	\(\chi_{9633}(521, \cdot)\)	n/a	28992	24
9633.2.fa	\(\chi_{9633}(107, \cdot)\)	n/a	29040	24
9633.2.ff	\(\chi_{9633}(113, \cdot)\)	n/a	29040	24
9633.2.fg	\(\chi_{9633}(49, \cdot)\)	n/a	14544	24
9633.2.fi	\(\chi_{9633}(179, \cdot)\)	n/a	29040	24
9633.2.fk	\(\chi_{9633}(16, \cdot)\)	n/a	43704	72
9633.2.fl	\(\chi_{9633}(118, \cdot)\)	n/a	43632	72
9633.2.fm	\(\chi_{9633}(100, \cdot)\)	n/a	43704	72
9633.2.fn	\(\chi_{9633}(46, \cdot)\)	n/a	29088	48
9633.2.fq	\(\chi_{9633}(83, \cdot)\)	n/a	57984	48
9633.2.fs	\(\chi_{9633}(20, \cdot)\)	n/a	52416	48
9633.2.fu	\(\chi_{9633}(31, \cdot)\)	n/a	29184	48
9633.2.fw	\(\chi_{9633}(37, \cdot)\)	n/a	29088	48
9633.2.fx	\(\chi_{9633}(197, \cdot)\)	n/a	58080	48
9633.2.fz	\(\chi_{9633}(11, \cdot)\)	n/a	58080	48
9633.2.gb	\(\chi_{9633}(202, \cdot)\)	n/a	29088	48
9633.2.gf	\(\chi_{9633}(185, \cdot)\)	n/a	87048	72
9633.2.gg	\(\chi_{9633}(43, \cdot)\)	n/a	43704	72
9633.2.gh	\(\chi_{9633}(25, \cdot)\)	n/a	43632	72
9633.2.gi	\(\chi_{9633}(116, \cdot)\)	n/a	87120	72
9633.2.gj	\(\chi_{9633}(173, \cdot)\)	n/a	87048	72
9633.2.gs	\(\chi_{9633}(29, \cdot)\)	n/a	87048	72
9633.2.gt	\(\chi_{9633}(14, \cdot)\)	n/a	87120	72
9633.2.gu	\(\chi_{9633}(413, \cdot)\)	n/a	87048	72
9633.2.gv	\(\chi_{9633}(4, \cdot)\)	n/a	43704	72
9633.2.gy	\(\chi_{9633}(5, \cdot)\)	n/a	174240	144
9633.2.gz	\(\chi_{9633}(34, \cdot)\)	n/a	87264	144
9633.2.hc	\(\chi_{9633}(149, \cdot)\)	n/a	174096	144
9633.2.hd	\(\chi_{9633}(67, \cdot)\)	n/a	87408	144
9633.2.hi	\(\chi_{9633}(124, \cdot)\)	n/a	87408	144
9633.2.hj	\(\chi_{9633}(119, \cdot)\)	n/a	174096	144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9633))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9633)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(741))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3211))\)\(^{\oplus 2}\)