Space of modular forms of level 2912 and weight 2

• Label: 2912.2
• Level: 2912
• Weight: 2
• Dimension: 136348
• Nonzero newspaces: 100
• Sturm bound: 1032192
• Trace bound: 41

Defining parameters

Level:	\( N \)	=	\( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 100 \)
Sturm bound:			\(1032192\)
Trace bound:			\(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2912))\).

	Total	New	Old
Modular forms	262656	138548	124108
Cusp forms	253441	136348	117093
Eisenstein series	9215	2200	7015

Trace form

136348 * q - 160 * q^2 - 124 * q^3 - 160 * q^4 - 168 * q^5 - 160 * q^6 - 152 * q^7 - 400 * q^8 - 244 * q^9 - 128 * q^10 - 124 * q^11 - 96 * q^12 - 164 * q^13 - 408 * q^14 - 288 * q^15 - 80 * q^16 - 64 * q^17 - 80 * q^18 - 124 * q^19 - 96 * q^20 - 200 * q^21 - 352 * q^22 - 92 * q^23 - 208 * q^24 - 236 * q^25 - 216 * q^26 - 160 * q^27 - 240 * q^28 - 440 * q^29 - 288 * q^30 - 44 * q^31 - 240 * q^32 - 392 * q^33 - 208 * q^34 - 104 * q^35 - 512 * q^36 - 168 * q^37 - 128 * q^38 - 68 * q^39 - 304 * q^40 - 192 * q^41 - 160 * q^42 - 248 * q^43 + 8 * q^45 - 32 * q^46 - 36 * q^47 + 48 * q^48 - 28 * q^49 - 240 * q^50 + 4 * q^51 - 160 * q^52 - 136 * q^53 - 112 * q^54 - 168 * q^55 - 176 * q^56 - 400 * q^57 - 176 * q^58 - 156 * q^59 - 176 * q^60 + 24 * q^61 - 240 * q^62 - 120 * q^63 - 544 * q^64 - 412 * q^65 - 448 * q^66 - 212 * q^67 - 80 * q^68 + 64 * q^69 - 224 * q^70 - 408 * q^71 - 64 * q^72 - 256 * q^73 - 96 * q^74 - 40 * q^75 - 160 * q^76 - 168 * q^77 - 360 * q^78 - 252 * q^79 - 176 * q^80 - 108 * q^81 - 160 * q^82 + 48 * q^83 - 160 * q^84 - 288 * q^85 - 240 * q^86 + 280 * q^87 - 144 * q^88 - 400 * q^90 - 64 * q^91 - 1072 * q^92 + 80 * q^93 - 400 * q^94 + 284 * q^95 - 624 * q^96 - 320 * q^97 - 576 * q^98 + 168 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2912))\)

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
2912.2.a	\(\chi_{2912}(1, \cdot)\)	2912.2.a.a	1	1
		2912.2.a.b	1
		2912.2.a.c	1
		2912.2.a.d	1
		2912.2.a.e	1
		2912.2.a.f	1
		2912.2.a.g	3
		2912.2.a.h	3
		2912.2.a.i	3
		2912.2.a.j	3
		2912.2.a.k	3
		2912.2.a.l	3
		2912.2.a.m	4
		2912.2.a.n	4
		2912.2.a.o	4
		2912.2.a.p	4
		2912.2.a.q	5
		2912.2.a.r	5
		2912.2.a.s	5
		2912.2.a.t	5
		2912.2.a.u	6
		2912.2.a.v	6
2912.2.b	\(\chi_{2912}(1455, \cdot)\)	n/a	108	1
2912.2.c	\(\chi_{2912}(1457, \cdot)\)	2912.2.c.a	34	1
		2912.2.c.b	38
2912.2.h	\(\chi_{2912}(2575, \cdot)\)	2912.2.h.a	48	1
		2912.2.h.b	48
2912.2.i	\(\chi_{2912}(337, \cdot)\)	2912.2.i.a	84	1
2912.2.j	\(\chi_{2912}(1119, \cdot)\)	2912.2.j.a	48	1
		2912.2.j.b	48
2912.2.k	\(\chi_{2912}(1793, \cdot)\)	2912.2.k.a	2	1
		2912.2.k.b	2
		2912.2.k.c	4
		2912.2.k.d	4
		2912.2.k.e	4
		2912.2.k.f	4
		2912.2.k.g	8
		2912.2.k.h	12
		2912.2.k.i	14
		2912.2.k.j	14
		2912.2.k.k	16
2912.2.p	\(\chi_{2912}(2911, \cdot)\)	n/a	112	1
2912.2.q	\(\chi_{2912}(289, \cdot)\)	n/a	224	2
2912.2.r	\(\chi_{2912}(417, \cdot)\)	n/a	192	2
2912.2.s	\(\chi_{2912}(1121, \cdot)\)	n/a	168	2
2912.2.t	\(\chi_{2912}(737, \cdot)\)	n/a	224	2
2912.2.v	\(\chi_{2912}(1695, \cdot)\)	n/a	168	2
2912.2.w	\(\chi_{2912}(993, \cdot)\)	n/a	224	2
2912.2.y	\(\chi_{2912}(1191, \cdot)\)	None	0	2
2912.2.z	\(\chi_{2912}(489, \cdot)\)	None	0	2
2912.2.bd	\(\chi_{2912}(391, \cdot)\)	None	0	2
2912.2.be	\(\chi_{2912}(1065, \cdot)\)	None	0	2
2912.2.bh	\(\chi_{2912}(727, \cdot)\)	None	0	2
2912.2.bi	\(\chi_{2912}(729, \cdot)\)	None	0	2
2912.2.bm	\(\chi_{2912}(967, \cdot)\)	None	0	2
2912.2.bn	\(\chi_{2912}(265, \cdot)\)	None	0	2
2912.2.bp	\(\chi_{2912}(239, \cdot)\)	n/a	168	2
2912.2.bq	\(\chi_{2912}(2449, \cdot)\)	n/a	216	2
2912.2.bu	\(\chi_{2912}(849, \cdot)\)	n/a	216	2
2912.2.bv	\(\chi_{2912}(367, \cdot)\)	n/a	216	2
2912.2.bw	\(\chi_{2912}(81, \cdot)\)	n/a	216	2
2912.2.bx	\(\chi_{2912}(719, \cdot)\)	n/a	216	2
2912.2.cc	\(\chi_{2912}(225, \cdot)\)	n/a	168	2
2912.2.cd	\(\chi_{2912}(2239, \cdot)\)	n/a	224	2
2912.2.ce	\(\chi_{2912}(927, \cdot)\)	n/a	224	2
2912.2.cf	\(\chi_{2912}(831, \cdot)\)	n/a	224	2
2912.2.co	\(\chi_{2912}(961, \cdot)\)	n/a	224	2
2912.2.cp	\(\chi_{2912}(703, \cdot)\)	n/a	192	2
2912.2.cq	\(\chi_{2912}(159, \cdot)\)	n/a	224	2
2912.2.cr	\(\chi_{2912}(641, \cdot)\)	n/a	224	2
2912.2.cs	\(\chi_{2912}(1343, \cdot)\)	n/a	224	2
2912.2.cx	\(\chi_{2912}(113, \cdot)\)	n/a	168	2
2912.2.cy	\(\chi_{2912}(335, \cdot)\)	n/a	216	2
2912.2.cz	\(\chi_{2912}(753, \cdot)\)	n/a	216	2
2912.2.da	\(\chi_{2912}(495, \cdot)\)	n/a	192	2
2912.2.db	\(\chi_{2912}(815, \cdot)\)	n/a	216	2
2912.2.dc	\(\chi_{2912}(1297, \cdot)\)	n/a	216	2
2912.2.dl	\(\chi_{2912}(1167, \cdot)\)	n/a	216	2
2912.2.dm	\(\chi_{2912}(529, \cdot)\)	n/a	216	2
2912.2.dn	\(\chi_{2912}(625, \cdot)\)	n/a	192	2
2912.2.do	\(\chi_{2912}(1039, \cdot)\)	n/a	216	2
2912.2.dp	\(\chi_{2912}(1681, \cdot)\)	n/a	168	2
2912.2.dq	\(\chi_{2912}(783, \cdot)\)	n/a	216	2
2912.2.dv	\(\chi_{2912}(1375, \cdot)\)	n/a	224	2
2912.2.dw	\(\chi_{2912}(1089, \cdot)\)	n/a	224	2
2912.2.dx	\(\chi_{2912}(607, \cdot)\)	n/a	224	2
2912.2.eb	\(\chi_{2912}(365, \cdot)\)	n/a	1152	4
2912.2.ed	\(\chi_{2912}(363, \cdot)\)	n/a	1776	4
2912.2.ee	\(\chi_{2912}(853, \cdot)\)	n/a	1776	4
2912.2.eh	\(\chi_{2912}(125, \cdot)\)	n/a	1776	4
2912.2.ei	\(\chi_{2912}(99, \cdot)\)	n/a	1344	4
2912.2.el	\(\chi_{2912}(827, \cdot)\)	n/a	1344	4
2912.2.em	\(\chi_{2912}(701, \cdot)\)	n/a	1344	4
2912.2.eo	\(\chi_{2912}(27, \cdot)\)	n/a	1536	4
2912.2.er	\(\chi_{2912}(33, \cdot)\)	n/a	448	4
2912.2.es	\(\chi_{2912}(1887, \cdot)\)	n/a	448	4
2912.2.ev	\(\chi_{2912}(1775, \cdot)\)	n/a	432	4
2912.2.ey	\(\chi_{2912}(657, \cdot)\)	n/a	432	4
2912.2.ez	\(\chi_{2912}(369, \cdot)\)	n/a	432	4
2912.2.fa	\(\chi_{2912}(15, \cdot)\)	n/a	336	4
2912.2.fb	\(\chi_{2912}(655, \cdot)\)	n/a	432	4
2912.2.fe	\(\chi_{2912}(145, \cdot)\)	n/a	432	4
2912.2.fi	\(\chi_{2912}(713, \cdot)\)	None	0	4
2912.2.fj	\(\chi_{2912}(1415, \cdot)\)	None	0	4
2912.2.fm	\(\chi_{2912}(201, \cdot)\)	None	0	4
2912.2.fn	\(\chi_{2912}(375, \cdot)\)	None	0	4
2912.2.fo	\(\chi_{2912}(487, \cdot)\)	None	0	4
2912.2.fp	\(\chi_{2912}(1097, \cdot)\)	None	0	4
2912.2.fq	\(\chi_{2912}(135, \cdot)\)	None	0	4
2912.2.fr	\(\chi_{2912}(89, \cdot)\)	None	0	4
2912.2.fx	\(\chi_{2912}(9, \cdot)\)	None	0	4
2912.2.fy	\(\chi_{2912}(647, \cdot)\)	None	0	4
2912.2.gb	\(\chi_{2912}(121, \cdot)\)	None	0	4
2912.2.gc	\(\chi_{2912}(1095, \cdot)\)	None	0	4
2912.2.gf	\(\chi_{2912}(25, \cdot)\)	None	0	4
2912.2.gg	\(\chi_{2912}(1223, \cdot)\)	None	0	4
2912.2.gj	\(\chi_{2912}(199, \cdot)\)	None	0	4
2912.2.gl	\(\chi_{2912}(393, \cdot)\)	None	0	4
2912.2.gm	\(\chi_{2912}(615, \cdot)\)	None	0	4
2912.2.go	\(\chi_{2912}(1017, \cdot)\)	None	0	4
2912.2.gr	\(\chi_{2912}(87, \cdot)\)	None	0	4
2912.2.gt	\(\chi_{2912}(953, \cdot)\)	None	0	4
2912.2.gu	\(\chi_{2912}(55, \cdot)\)	None	0	4
2912.2.gw	\(\chi_{2912}(569, \cdot)\)	None	0	4
2912.2.gz	\(\chi_{2912}(1145, \cdot)\)	None	0	4
2912.2.ha	\(\chi_{2912}(103, \cdot)\)	None	0	4
2912.2.hc	\(\chi_{2912}(297, \cdot)\)	None	0	4
2912.2.hd	\(\chi_{2912}(695, \cdot)\)	None	0	4
2912.2.hk	\(\chi_{2912}(583, \cdot)\)	None	0	4
2912.2.hl	\(\chi_{2912}(73, \cdot)\)	None	0	4
2912.2.hm	\(\chi_{2912}(359, \cdot)\)	None	0	4
2912.2.hn	\(\chi_{2912}(409, \cdot)\)	None	0	4
2912.2.ho	\(\chi_{2912}(41, \cdot)\)	None	0	4
2912.2.hp	\(\chi_{2912}(71, \cdot)\)	None	0	4
2912.2.ht	\(\chi_{2912}(319, \cdot)\)	n/a	448	4
2912.2.hw	\(\chi_{2912}(97, \cdot)\)	n/a	448	4
2912.2.hx	\(\chi_{2912}(577, \cdot)\)	n/a	448	4
2912.2.hy	\(\chi_{2912}(799, \cdot)\)	n/a	336	4
2912.2.hz	\(\chi_{2912}(863, \cdot)\)	n/a	448	4
2912.2.ic	\(\chi_{2912}(1601, \cdot)\)	n/a	448	4
2912.2.if	\(\chi_{2912}(1489, \cdot)\)	n/a	432	4
2912.2.ig	\(\chi_{2912}(431, \cdot)\)	n/a	432	4
2912.2.ii	\(\chi_{2912}(467, \cdot)\)	n/a	3552	8
2912.2.ik	\(\chi_{2912}(53, \cdot)\)	n/a	3072	8
2912.2.in	\(\chi_{2912}(205, \cdot)\)	n/a	3552	8
2912.2.io	\(\chi_{2912}(3, \cdot)\)	n/a	3552	8
2912.2.ir	\(\chi_{2912}(139, \cdot)\)	n/a	3552	8
2912.2.it	\(\chi_{2912}(309, \cdot)\)	n/a	2688	8
2912.2.iu	\(\chi_{2912}(485, \cdot)\)	n/a	3552	8
2912.2.ix	\(\chi_{2912}(451, \cdot)\)	n/a	3552	8
2912.2.iy	\(\chi_{2912}(605, \cdot)\)	n/a	3552	8
2912.2.jb	\(\chi_{2912}(45, \cdot)\)	n/a	3552	8
2912.2.jc	\(\chi_{2912}(515, \cdot)\)	n/a	3552	8
2912.2.je	\(\chi_{2912}(267, \cdot)\)	n/a	2688	8
2912.2.jf	\(\chi_{2912}(11, \cdot)\)	n/a	3552	8
2912.2.jk	\(\chi_{2912}(163, \cdot)\)	n/a	3552	8
2912.2.jl	\(\chi_{2912}(323, \cdot)\)	n/a	2688	8
2912.2.jn	\(\chi_{2912}(291, \cdot)\)	n/a	3552	8
2912.2.jo	\(\chi_{2912}(229, \cdot)\)	n/a	3552	8
2912.2.jq	\(\chi_{2912}(349, \cdot)\)	n/a	3552	8
2912.2.jr	\(\chi_{2912}(397, \cdot)\)	n/a	3552	8
2912.2.jw	\(\chi_{2912}(661, \cdot)\)	n/a	3552	8
2912.2.jx	\(\chi_{2912}(293, \cdot)\)	n/a	3552	8
2912.2.jz	\(\chi_{2912}(5, \cdot)\)	n/a	3552	8
2912.2.ka	\(\chi_{2912}(219, \cdot)\)	n/a	3552	8
2912.2.kd	\(\chi_{2912}(123, \cdot)\)	n/a	3552	8
2912.2.ke	\(\chi_{2912}(165, \cdot)\)	n/a	3552	8
2912.2.kg	\(\chi_{2912}(251, \cdot)\)	n/a	3552	8
2912.2.kj	\(\chi_{2912}(283, \cdot)\)	n/a	3552	8
2912.2.kl	\(\chi_{2912}(373, \cdot)\)	n/a	3552	8
2912.2.km	\(\chi_{2912}(29, \cdot)\)	n/a	2688	8
2912.2.ko	\(\chi_{2912}(75, \cdot)\)	n/a	3552	8
2912.2.kr	\(\chi_{2912}(131, \cdot)\)	n/a	3072	8
2912.2.kt	\(\chi_{2912}(389, \cdot)\)	n/a	3552	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2912))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2912)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2912))\)\(^{\oplus 1}\)