Space of modular forms of level 2184 and weight 2

• Label: 2184.2
• Level: 2184
• Weight: 2
• Dimension: 51104
• Nonzero newspaces: 90
• Sturm bound: 516096
• Trace bound: 24

Defining parameters

Level:	\( N \)	=	\( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 90 \)
Sturm bound:			\(516096\)
Trace bound:			\(24\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2184))\).

	Total	New	Old
Modular forms	132480	51984	80496
Cusp forms	125569	51104	74465
Eisenstein series	6911	880	6031

Trace form

51104 * q - 8 * q^2 - 48 * q^3 - 88 * q^4 - 8 * q^5 - 28 * q^6 - 104 * q^7 + 16 * q^8 - 96 * q^9 - 56 * q^10 - 8 * q^11 - 4 * q^12 - 16 * q^13 + 8 * q^14 - 96 * q^15 - 72 * q^16 - 44 * q^17 - 60 * q^18 - 120 * q^19 + 40 * q^20 - 24 * q^21 - 104 * q^22 + 24 * q^23 - 12 * q^24 - 168 * q^25 + 44 * q^26 - 96 * q^27 + 96 * q^28 - 36 * q^29 + 44 * q^30 + 24 * q^31 + 152 * q^32 - 44 * q^33 + 152 * q^34 + 48 * q^35 - 56 * q^36 + 36 * q^37 + 104 * q^38 + 12 * q^39 + 176 * q^40 + 28 * q^41 - 40 * q^42 - 16 * q^43 + 144 * q^44 + 112 * q^45 + 256 * q^46 + 192 * q^47 + 4 * q^48 - 108 * q^49 + 256 * q^50 + 216 * q^51 + 272 * q^52 + 208 * q^53 - 204 * q^54 + 328 * q^55 + 32 * q^56 - 88 * q^57 + 144 * q^58 + 304 * q^59 + 172 * q^61 + 8 * q^62 + 104 * q^63 - 136 * q^64 + 76 * q^65 - 148 * q^66 + 120 * q^67 - 120 * q^68 + 56 * q^69 - 88 * q^70 + 128 * q^71 - 216 * q^72 - 232 * q^73 + 64 * q^74 + 104 * q^75 - 168 * q^76 - 72 * q^77 - 176 * q^78 - 216 * q^79 - 80 * q^81 - 216 * q^82 - 112 * q^83 - 364 * q^84 - 124 * q^85 - 224 * q^86 - 248 * q^88 - 8 * q^89 - 592 * q^90 - 24 * q^91 - 312 * q^92 + 52 * q^93 - 504 * q^94 + 208 * q^95 - 660 * q^96 + 80 * q^97 - 344 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2184))\)

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
2184.2.a	\(\chi_{2184}(1, \cdot)\)	2184.2.a.a	1	1
		2184.2.a.b	1
		2184.2.a.c	1
		2184.2.a.d	1
		2184.2.a.e	1
		2184.2.a.f	1
		2184.2.a.g	1
		2184.2.a.h	1
		2184.2.a.i	1
		2184.2.a.j	1
		2184.2.a.k	1
		2184.2.a.l	1
		2184.2.a.m	1
		2184.2.a.n	2
		2184.2.a.o	2
		2184.2.a.p	2
		2184.2.a.q	2
		2184.2.a.r	2
		2184.2.a.s	3
		2184.2.a.t	3
		2184.2.a.u	3
		2184.2.a.v	4
2184.2.b	\(\chi_{2184}(1819, \cdot)\)	n/a	224	1
2184.2.e	\(\chi_{2184}(391, \cdot)\)	None	0	1
2184.2.g	\(\chi_{2184}(1093, \cdot)\)	n/a	144	1
2184.2.h	\(\chi_{2184}(337, \cdot)\)	2184.2.h.a	2	1
		2184.2.h.b	2
		2184.2.h.c	4
		2184.2.h.d	6
		2184.2.h.e	10
		2184.2.h.f	10
		2184.2.h.g	10
2184.2.j	\(\chi_{2184}(911, \cdot)\)	None	0	1
2184.2.m	\(\chi_{2184}(155, \cdot)\)	n/a	336	1
2184.2.o	\(\chi_{2184}(545, \cdot)\)	n/a	112	1
2184.2.p	\(\chi_{2184}(1301, \cdot)\)	n/a	384	1
2184.2.s	\(\chi_{2184}(1247, \cdot)\)	None	0	1
2184.2.t	\(\chi_{2184}(2003, \cdot)\)	n/a	288	1
2184.2.v	\(\chi_{2184}(209, \cdot)\)	2184.2.v.a	48	1
		2184.2.v.b	48
2184.2.y	\(\chi_{2184}(1637, \cdot)\)	n/a	440	1
2184.2.ba	\(\chi_{2184}(1483, \cdot)\)	n/a	192	1
2184.2.bb	\(\chi_{2184}(727, \cdot)\)	None	0	1
2184.2.bd	\(\chi_{2184}(1429, \cdot)\)	n/a	168	1
2184.2.bg	\(\chi_{2184}(625, \cdot)\)	2184.2.bg.a	2	2
		2184.2.bg.b	2
		2184.2.bg.c	2
		2184.2.bg.d	2
		2184.2.bg.e	4
		2184.2.bg.f	4
		2184.2.bg.g	6
		2184.2.bg.h	6
		2184.2.bg.i	8
		2184.2.bg.j	10
		2184.2.bg.k	12
		2184.2.bg.l	12
		2184.2.bg.m	12
		2184.2.bg.n	14
2184.2.bh	\(\chi_{2184}(289, \cdot)\)	n/a	112	2
2184.2.bi	\(\chi_{2184}(1465, \cdot)\)	n/a	112	2
2184.2.bj	\(\chi_{2184}(841, \cdot)\)	2184.2.bj.a	2	2
		2184.2.bj.b	2
		2184.2.bj.c	2
		2184.2.bj.d	2
		2184.2.bj.e	2
		2184.2.bj.f	4
		2184.2.bj.g	6
		2184.2.bj.h	8
		2184.2.bj.i	8
		2184.2.bj.j	8
		2184.2.bj.k	8
		2184.2.bj.l	8
		2184.2.bj.m	10
		2184.2.bj.n	10
2184.2.bk	\(\chi_{2184}(671, \cdot)\)	None	0	2
2184.2.bm	\(\chi_{2184}(83, \cdot)\)	n/a	880	2
2184.2.bo	\(\chi_{2184}(1555, \cdot)\)	n/a	336	2
2184.2.bq	\(\chi_{2184}(463, \cdot)\)	None	0	2
2184.2.bt	\(\chi_{2184}(853, \cdot)\)	n/a	448	2
2184.2.bv	\(\chi_{2184}(265, \cdot)\)	n/a	112	2
2184.2.bx	\(\chi_{2184}(281, \cdot)\)	n/a	168	2
2184.2.bz	\(\chi_{2184}(1373, \cdot)\)	n/a	672	2
2184.2.ca	\(\chi_{2184}(965, \cdot)\)	n/a	880	2
2184.2.cd	\(\chi_{2184}(881, \cdot)\)	n/a	224	2
2184.2.cf	\(\chi_{2184}(491, \cdot)\)	n/a	672	2
2184.2.cg	\(\chi_{2184}(575, \cdot)\)	None	0	2
2184.2.ci	\(\chi_{2184}(673, \cdot)\)	2184.2.ci.a	20	2
		2184.2.ci.b	20
		2184.2.ci.c	24
		2184.2.ci.d	24
2184.2.cl	\(\chi_{2184}(757, \cdot)\)	n/a	336	2
2184.2.cn	\(\chi_{2184}(55, \cdot)\)	None	0	2
2184.2.co	\(\chi_{2184}(979, \cdot)\)	n/a	448	2
2184.2.cq	\(\chi_{2184}(101, \cdot)\)	n/a	880	2
2184.2.ct	\(\chi_{2184}(185, \cdot)\)	n/a	224	2
2184.2.cv	\(\chi_{2184}(1283, \cdot)\)	n/a	880	2
2184.2.cw	\(\chi_{2184}(1031, \cdot)\)	None	0	2
2184.2.cz	\(\chi_{2184}(199, \cdot)\)	None	0	2
2184.2.da	\(\chi_{2184}(451, \cdot)\)	n/a	448	2
2184.2.dd	\(\chi_{2184}(1117, \cdot)\)	n/a	448	2
2184.2.df	\(\chi_{2184}(859, \cdot)\)	n/a	384	2
2184.2.di	\(\chi_{2184}(103, \cdot)\)	None	0	2
2184.2.dl	\(\chi_{2184}(205, \cdot)\)	n/a	448	2
2184.2.dn	\(\chi_{2184}(107, \cdot)\)	n/a	880	2
2184.2.do	\(\chi_{2184}(23, \cdot)\)	None	0	2
2184.2.dr	\(\chi_{2184}(521, \cdot)\)	n/a	192	2
2184.2.ds	\(\chi_{2184}(1013, \cdot)\)	n/a	880	2
2184.2.du	\(\chi_{2184}(935, \cdot)\)	None	0	2
2184.2.dx	\(\chi_{2184}(443, \cdot)\)	n/a	768	2
2184.2.dy	\(\chi_{2184}(1109, \cdot)\)	n/a	880	2
2184.2.eb	\(\chi_{2184}(1361, \cdot)\)	n/a	224	2
2184.2.ee	\(\chi_{2184}(1213, \cdot)\)	n/a	448	2
2184.2.eg	\(\chi_{2184}(1375, \cdot)\)	None	0	2
2184.2.eh	\(\chi_{2184}(1459, \cdot)\)	n/a	448	2
2184.2.ek	\(\chi_{2184}(121, \cdot)\)	n/a	112	2
2184.2.el	\(\chi_{2184}(373, \cdot)\)	n/a	448	2
2184.2.en	\(\chi_{2184}(367, \cdot)\)	None	0	2
2184.2.eq	\(\chi_{2184}(283, \cdot)\)	n/a	448	2
2184.2.er	\(\chi_{2184}(1115, \cdot)\)	n/a	880	2
2184.2.eu	\(\chi_{2184}(1199, \cdot)\)	None	0	2
2184.2.ev	\(\chi_{2184}(857, \cdot)\)	n/a	224	2
2184.2.ey	\(\chi_{2184}(677, \cdot)\)	n/a	768	2
2184.2.fa	\(\chi_{2184}(599, \cdot)\)	None	0	2
2184.2.fb	\(\chi_{2184}(779, \cdot)\)	n/a	880	2
2184.2.fe	\(\chi_{2184}(269, \cdot)\)	n/a	880	2
2184.2.ff	\(\chi_{2184}(17, \cdot)\)	n/a	224	2
2184.2.fh	\(\chi_{2184}(1543, \cdot)\)	None	0	2
2184.2.fk	\(\chi_{2184}(1291, \cdot)\)	n/a	448	2
2184.2.fl	\(\chi_{2184}(781, \cdot)\)	n/a	384	2
2184.2.fo	\(\chi_{2184}(25, \cdot)\)	n/a	112	2
2184.2.fq	\(\chi_{2184}(1195, \cdot)\)	n/a	448	2
2184.2.fr	\(\chi_{2184}(703, \cdot)\)	None	0	2
2184.2.fu	\(\chi_{2184}(1297, \cdot)\)	n/a	112	2
2184.2.fv	\(\chi_{2184}(1381, \cdot)\)	n/a	448	2
2184.2.fy	\(\chi_{2184}(1277, \cdot)\)	n/a	880	2
2184.2.fz	\(\chi_{2184}(1193, \cdot)\)	n/a	224	2
2184.2.gb	\(\chi_{2184}(179, \cdot)\)	n/a	880	2
2184.2.ge	\(\chi_{2184}(191, \cdot)\)	None	0	2
2184.2.gg	\(\chi_{2184}(589, \cdot)\)	n/a	336	2
2184.2.gi	\(\chi_{2184}(1063, \cdot)\)	None	0	2
2184.2.gl	\(\chi_{2184}(139, \cdot)\)	n/a	448	2
2184.2.gn	\(\chi_{2184}(797, \cdot)\)	n/a	880	2
2184.2.go	\(\chi_{2184}(1049, \cdot)\)	n/a	224	2
2184.2.gq	\(\chi_{2184}(659, \cdot)\)	n/a	672	2
2184.2.gt	\(\chi_{2184}(407, \cdot)\)	None	0	2
2184.2.gv	\(\chi_{2184}(59, \cdot)\)	n/a	1760	4
2184.2.gx	\(\chi_{2184}(1055, \cdot)\)	None	0	4
2184.2.gz	\(\chi_{2184}(319, \cdot)\)	None	0	4
2184.2.hb	\(\chi_{2184}(1003, \cdot)\)	n/a	896	4
2184.2.hd	\(\chi_{2184}(197, \cdot)\)	n/a	1344	4
2184.2.hf	\(\chi_{2184}(449, \cdot)\)	n/a	336	4
2184.2.hg	\(\chi_{2184}(473, \cdot)\)	n/a	448	4
2184.2.hi	\(\chi_{2184}(149, \cdot)\)	n/a	1760	4
2184.2.hk	\(\chi_{2184}(977, \cdot)\)	n/a	448	4
2184.2.hm	\(\chi_{2184}(317, \cdot)\)	n/a	1760	4
2184.2.hp	\(\chi_{2184}(97, \cdot)\)	n/a	224	4
2184.2.hr	\(\chi_{2184}(349, \cdot)\)	n/a	896	4
2184.2.hs	\(\chi_{2184}(229, \cdot)\)	n/a	896	4
2184.2.hu	\(\chi_{2184}(1081, \cdot)\)	n/a	224	4
2184.2.hw	\(\chi_{2184}(397, \cdot)\)	n/a	896	4
2184.2.hy	\(\chi_{2184}(73, \cdot)\)	n/a	224	4
2184.2.ia	\(\chi_{2184}(631, \cdot)\)	None	0	4
2184.2.ic	\(\chi_{2184}(379, \cdot)\)	n/a	672	4
2184.2.if	\(\chi_{2184}(499, \cdot)\)	n/a	896	4
2184.2.ih	\(\chi_{2184}(1159, \cdot)\)	None	0	4
2184.2.ij	\(\chi_{2184}(67, \cdot)\)	n/a	896	4
2184.2.il	\(\chi_{2184}(151, \cdot)\)	None	0	4
2184.2.im	\(\chi_{2184}(587, \cdot)\)	n/a	1760	4
2184.2.io	\(\chi_{2184}(167, \cdot)\)	None	0	4
2184.2.ir	\(\chi_{2184}(47, \cdot)\)	None	0	4
2184.2.it	\(\chi_{2184}(899, \cdot)\)	n/a	1760	4
2184.2.iv	\(\chi_{2184}(215, \cdot)\)	None	0	4
2184.2.ix	\(\chi_{2184}(395, \cdot)\)	n/a	1760	4
2184.2.iy	\(\chi_{2184}(145, \cdot)\)	n/a	224	4
2184.2.ja	\(\chi_{2184}(1237, \cdot)\)	n/a	896	4
2184.2.jc	\(\chi_{2184}(821, \cdot)\)	n/a	1760	4
2184.2.je	\(\chi_{2184}(137, \cdot)\)	n/a	448	4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2184)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1092))\)\(^{\oplus 2}\)