Space of modular forms of level 2128 and weight 2

• Label: 2128.2
• Level: 2128
• Weight: 2
• Dimension: 73340
• Nonzero newspaces: 64
• Sturm bound: 552960
• Trace bound: 53

Defining parameters

Level:	\( N \)	=	\( 2128 = 2^{4} \cdot 7 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 64 \)
Sturm bound:			\(552960\)
Trace bound:			\(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2128))\).

	Total	New	Old
Modular forms	141264	74872	66392
Cusp forms	135217	73340	61877
Eisenstein series	6047	1532	4515

Trace form

73340 * q - 128 * q^2 - 98 * q^3 - 120 * q^4 - 158 * q^5 - 104 * q^6 - 117 * q^7 - 296 * q^8 - 30 * q^9 - 120 * q^10 - 82 * q^11 - 136 * q^12 - 152 * q^13 - 164 * q^14 - 218 * q^15 - 152 * q^16 - 286 * q^17 - 112 * q^18 - 81 * q^19 - 248 * q^20 - 163 * q^21 - 312 * q^22 - 54 * q^23 - 120 * q^24 + 18 * q^25 - 104 * q^26 - 80 * q^27 - 140 * q^28 - 342 * q^29 - 136 * q^30 - 106 * q^31 - 88 * q^32 - 238 * q^33 - 104 * q^34 - 89 * q^35 - 328 * q^36 - 84 * q^37 - 156 * q^38 - 204 * q^39 - 152 * q^40 - 24 * q^41 - 300 * q^42 - 206 * q^43 - 232 * q^44 - 220 * q^45 - 192 * q^46 - 62 * q^47 - 328 * q^48 - 407 * q^49 - 504 * q^50 - 134 * q^51 - 352 * q^52 - 286 * q^53 - 456 * q^54 - 168 * q^55 - 340 * q^56 - 180 * q^57 - 480 * q^58 - 162 * q^59 - 456 * q^60 - 246 * q^61 - 272 * q^62 - 97 * q^63 - 480 * q^64 - 176 * q^65 - 344 * q^66 + 62 * q^67 - 240 * q^68 - 96 * q^69 - 236 * q^70 - 66 * q^71 - 296 * q^72 + 234 * q^73 - 120 * q^74 + 246 * q^75 - 108 * q^76 - 208 * q^77 - 328 * q^78 + 246 * q^79 - 88 * q^80 + 100 * q^81 - 120 * q^82 + 112 * q^83 - 172 * q^84 - 134 * q^85 - 120 * q^86 + 216 * q^87 - 88 * q^88 + 210 * q^89 + 8 * q^90 - 163 * q^91 - 384 * q^92 + 58 * q^93 - 40 * q^94 - 159 * q^95 - 88 * q^96 - 232 * q^97 - 28 * q^98 - 470 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2128))\)

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
2128.2.a	\(\chi_{2128}(1, \cdot)\)	2128.2.a.a	1	1
		2128.2.a.b	2
		2128.2.a.c	2
		2128.2.a.d	2
		2128.2.a.e	2
		2128.2.a.f	2
		2128.2.a.g	2
		2128.2.a.h	2
		2128.2.a.i	2
		2128.2.a.j	2
		2128.2.a.k	2
		2128.2.a.l	2
		2128.2.a.m	2
		2128.2.a.n	2
		2128.2.a.o	2
		2128.2.a.p	3
		2128.2.a.q	3
		2128.2.a.r	3
		2128.2.a.s	3
		2128.2.a.t	4
		2128.2.a.u	4
		2128.2.a.v	5
2128.2.b	\(\chi_{2128}(1065, \cdot)\)	None	0	1
2128.2.e	\(\chi_{2128}(1975, \cdot)\)	None	0	1
2128.2.f	\(\chi_{2128}(265, \cdot)\)	None	0	1
2128.2.i	\(\chi_{2128}(951, \cdot)\)	None	0	1
2128.2.j	\(\chi_{2128}(2015, \cdot)\)	2128.2.j.a	2	1
		2128.2.j.b	2
		2128.2.j.c	2
		2128.2.j.d	2
		2128.2.j.e	12
		2128.2.j.f	12
		2128.2.j.g	20
		2128.2.j.h	20
2128.2.m	\(\chi_{2128}(1329, \cdot)\)	2128.2.m.a	2	1
		2128.2.m.b	4
		2128.2.m.c	4
		2128.2.m.d	4
		2128.2.m.e	8
		2128.2.m.f	16
		2128.2.m.g	16
		2128.2.m.h	24
2128.2.n	\(\chi_{2128}(911, \cdot)\)	2128.2.n.a	4	1
		2128.2.n.b	4
		2128.2.n.c	4
		2128.2.n.d	8
		2128.2.n.e	40
2128.2.q	\(\chi_{2128}(305, \cdot)\)	n/a	144	2
2128.2.r	\(\chi_{2128}(1569, \cdot)\)	n/a	120	2
2128.2.s	\(\chi_{2128}(1185, \cdot)\)	n/a	156	2
2128.2.t	\(\chi_{2128}(961, \cdot)\)	n/a	156	2
2128.2.u	\(\chi_{2128}(797, \cdot)\)	n/a	632	2
2128.2.v	\(\chi_{2128}(419, \cdot)\)	n/a	576	2
2128.2.ba	\(\chi_{2128}(533, \cdot)\)	n/a	432	2
2128.2.bb	\(\chi_{2128}(379, \cdot)\)	n/a	480	2
2128.2.bc	\(\chi_{2128}(311, \cdot)\)	None	0	2
2128.2.bf	\(\chi_{2128}(297, \cdot)\)	None	0	2
2128.2.bg	\(\chi_{2128}(487, \cdot)\)	None	0	2
2128.2.bj	\(\chi_{2128}(1033, \cdot)\)	None	0	2
2128.2.bk	\(\chi_{2128}(145, \cdot)\)	n/a	156	2
2128.2.bn	\(\chi_{2128}(159, \cdot)\)	n/a	160	2
2128.2.bp	\(\chi_{2128}(1247, \cdot)\)	n/a	120	2
2128.2.br	\(\chi_{2128}(303, \cdot)\)	n/a	160	2
2128.2.bv	\(\chi_{2128}(1455, \cdot)\)	n/a	160	2
2128.2.bx	\(\chi_{2128}(1025, \cdot)\)	n/a	156	2
2128.2.by	\(\chi_{2128}(495, \cdot)\)	n/a	144	2
2128.2.ca	\(\chi_{2128}(1665, \cdot)\)	n/a	156	2
2128.2.ce	\(\chi_{2128}(639, \cdot)\)	n/a	160	2
2128.2.cf	\(\chi_{2128}(711, \cdot)\)	None	0	2
2128.2.ci	\(\chi_{2128}(121, \cdot)\)	None	0	2
2128.2.ck	\(\chi_{2128}(601, \cdot)\)	None	0	2
2128.2.cm	\(\chi_{2128}(647, \cdot)\)	None	0	2
2128.2.cn	\(\chi_{2128}(873, \cdot)\)	None	0	2
2128.2.cp	\(\chi_{2128}(391, \cdot)\)	None	0	2
2128.2.cs	\(\chi_{2128}(505, \cdot)\)	None	0	2
2128.2.cu	\(\chi_{2128}(151, \cdot)\)	None	0	2
2128.2.cv	\(\chi_{2128}(457, \cdot)\)	None	0	2
2128.2.cx	\(\chi_{2128}(183, \cdot)\)	None	0	2
2128.2.cz	\(\chi_{2128}(87, \cdot)\)	None	0	2
2128.2.dc	\(\chi_{2128}(521, \cdot)\)	None	0	2
2128.2.df	\(\chi_{2128}(863, \cdot)\)	n/a	160	2
2128.2.dg	\(\chi_{2128}(369, \cdot)\)	n/a	156	2
2128.2.dj	\(\chi_{2128}(1375, \cdot)\)	n/a	160	2
2128.2.dk	\(\chi_{2128}(225, \cdot)\)	n/a	360	6
2128.2.dl	\(\chi_{2128}(81, \cdot)\)	n/a	468	6
2128.2.dm	\(\chi_{2128}(625, \cdot)\)	n/a	468	6
2128.2.dp	\(\chi_{2128}(429, \cdot)\)	n/a	1264	4
2128.2.dq	\(\chi_{2128}(331, \cdot)\)	n/a	1264	4
2128.2.dr	\(\chi_{2128}(829, \cdot)\)	n/a	1264	4
2128.2.ds	\(\chi_{2128}(467, \cdot)\)	n/a	1264	4
2128.2.dx	\(\chi_{2128}(115, \cdot)\)	n/a	1152	4
2128.2.dy	\(\chi_{2128}(341, \cdot)\)	n/a	1264	4
2128.2.dz	\(\chi_{2128}(107, \cdot)\)	n/a	1264	4
2128.2.ea	\(\chi_{2128}(715, \cdot)\)	n/a	960	4
2128.2.eb	\(\chi_{2128}(277, \cdot)\)	n/a	1264	4
2128.2.ec	\(\chi_{2128}(197, \cdot)\)	n/a	960	4
2128.2.el	\(\chi_{2128}(619, \cdot)\)	n/a	1264	4
2128.2.em	\(\chi_{2128}(83, \cdot)\)	n/a	1264	4
2128.2.en	\(\chi_{2128}(677, \cdot)\)	n/a	1264	4
2128.2.eo	\(\chi_{2128}(69, \cdot)\)	n/a	1264	4
2128.2.ep	\(\chi_{2128}(683, \cdot)\)	n/a	1264	4
2128.2.eq	\(\chi_{2128}(837, \cdot)\)	n/a	1152	4
2128.2.et	\(\chi_{2128}(271, \cdot)\)	n/a	480	6
2128.2.eu	\(\chi_{2128}(79, \cdot)\)	n/a	480	6
2128.2.ex	\(\chi_{2128}(409, \cdot)\)	None	0	6
2128.2.ey	\(\chi_{2128}(25, \cdot)\)	None	0	6
2128.2.fd	\(\chi_{2128}(97, \cdot)\)	n/a	468	6
2128.2.fg	\(\chi_{2128}(257, \cdot)\)	n/a	468	6
2128.2.fj	\(\chi_{2128}(55, \cdot)\)	None	0	6
2128.2.fk	\(\chi_{2128}(71, \cdot)\)	None	0	6
2128.2.fn	\(\chi_{2128}(375, \cdot)\)	None	0	6
2128.2.fo	\(\chi_{2128}(215, \cdot)\)	None	0	6
2128.2.fr	\(\chi_{2128}(15, \cdot)\)	n/a	360	6
2128.2.fs	\(\chi_{2128}(111, \cdot)\)	n/a	480	6
2128.2.fv	\(\chi_{2128}(47, \cdot)\)	n/a	480	6
2128.2.fw	\(\chi_{2128}(751, \cdot)\)	n/a	480	6
2128.2.fz	\(\chi_{2128}(169, \cdot)\)	None	0	6
2128.2.ga	\(\chi_{2128}(41, \cdot)\)	None	0	6
2128.2.gd	\(\chi_{2128}(89, \cdot)\)	None	0	6
2128.2.ge	\(\chi_{2128}(9, \cdot)\)	None	0	6
2128.2.gf	\(\chi_{2128}(33, \cdot)\)	n/a	468	6
2128.2.gi	\(\chi_{2128}(135, \cdot)\)	None	0	6
2128.2.gj	\(\chi_{2128}(199, \cdot)\)	None	0	6
2128.2.gq	\(\chi_{2128}(85, \cdot)\)	n/a	2880	12
2128.2.gr	\(\chi_{2128}(13, \cdot)\)	n/a	3792	12
2128.2.gs	\(\chi_{2128}(131, \cdot)\)	n/a	3792	12
2128.2.gt	\(\chi_{2128}(67, \cdot)\)	n/a	3792	12
2128.2.gu	\(\chi_{2128}(93, \cdot)\)	n/a	3792	12
2128.2.gv	\(\chi_{2128}(117, \cdot)\)	n/a	3792	12
2128.2.gw	\(\chi_{2128}(139, \cdot)\)	n/a	3792	12
2128.2.gx	\(\chi_{2128}(155, \cdot)\)	n/a	2880	12
2128.2.hg	\(\chi_{2128}(51, \cdot)\)	n/a	3792	12
2128.2.hh	\(\chi_{2128}(283, \cdot)\)	n/a	3792	12
2128.2.hi	\(\chi_{2128}(269, \cdot)\)	n/a	3792	12
2128.2.hj	\(\chi_{2128}(541, \cdot)\)	n/a	3792	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1064))\)\(^{\oplus 2}\)