Space of modular forms of level 2720 and weight 2

• Label: 2720.2
• Level: 2720
• Weight: 2
• Dimension: 112356
• Nonzero newspaces: 84
• Sturm bound: 884736
• Trace bound: 77

Defining parameters

Level:	\( N \)	=	\( 2720 = 2^{5} \cdot 5 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 84 \)
Sturm bound:			\(884736\)
Trace bound:			\(77\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2720))\).

	Total	New	Old
Modular forms	225280	114156	111124
Cusp forms	217089	112356	104733
Eisenstein series	8191	1800	6391

Trace form

112356 * q - 112 * q^2 - 88 * q^3 - 112 * q^4 - 172 * q^5 - 336 * q^6 - 88 * q^7 - 112 * q^8 - 172 * q^9 - 152 * q^10 - 256 * q^11 - 48 * q^12 - 88 * q^13 - 48 * q^14 - 120 * q^15 - 256 * q^16 - 52 * q^17 - 160 * q^18 - 80 * q^19 - 136 * q^20 - 336 * q^21 - 64 * q^22 - 56 * q^23 - 160 * q^24 - 260 * q^25 - 416 * q^26 + 32 * q^27 - 192 * q^28 - 136 * q^29 - 232 * q^30 - 144 * q^31 - 192 * q^32 - 208 * q^33 - 144 * q^34 - 176 * q^35 - 448 * q^36 - 40 * q^37 - 80 * q^38 + 64 * q^39 - 144 * q^40 - 392 * q^41 - 32 * q^42 + 8 * q^43 + 48 * q^44 - 52 * q^45 - 208 * q^46 - 24 * q^47 + 96 * q^48 - 12 * q^49 - 88 * q^50 - 264 * q^51 - 208 * q^52 + 24 * q^53 - 64 * q^54 - 152 * q^55 - 288 * q^56 - 208 * q^57 - 128 * q^58 - 208 * q^59 - 304 * q^60 - 248 * q^61 - 192 * q^62 - 296 * q^63 - 352 * q^64 - 504 * q^65 - 688 * q^66 - 264 * q^67 - 192 * q^68 - 304 * q^69 - 480 * q^70 - 448 * q^71 - 496 * q^72 - 312 * q^73 - 400 * q^74 - 304 * q^75 - 592 * q^76 - 240 * q^77 - 560 * q^78 - 192 * q^79 - 496 * q^80 - 380 * q^81 - 432 * q^82 - 8 * q^83 - 640 * q^84 - 260 * q^85 - 1056 * q^86 + 48 * q^87 - 448 * q^88 - 248 * q^89 - 624 * q^90 - 128 * q^91 - 544 * q^92 - 352 * q^93 - 288 * q^94 - 16 * q^95 - 576 * q^96 - 264 * q^97 - 288 * q^98 + 224 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2720))\)

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
2720.2.a	\(\chi_{2720}(1, \cdot)\)	2720.2.a.a	1	1
		2720.2.a.b	1
		2720.2.a.c	1
		2720.2.a.d	1
		2720.2.a.e	1
		2720.2.a.f	1
		2720.2.a.g	2
		2720.2.a.h	2
		2720.2.a.i	2
		2720.2.a.j	4
		2720.2.a.k	4
		2720.2.a.l	4
		2720.2.a.m	4
		2720.2.a.n	4
		2720.2.a.o	4
		2720.2.a.p	4
		2720.2.a.q	4
		2720.2.a.r	4
		2720.2.a.s	5
		2720.2.a.t	5
		2720.2.a.u	6
2720.2.c	\(\chi_{2720}(1121, \cdot)\)	2720.2.c.a	2	1
		2720.2.c.b	2
		2720.2.c.c	4
		2720.2.c.d	12
		2720.2.c.e	16
		2720.2.c.f	16
		2720.2.c.g	20
2720.2.e	\(\chi_{2720}(1089, \cdot)\)	2720.2.e.a	2	1
		2720.2.e.b	2
		2720.2.e.c	4
		2720.2.e.d	8
		2720.2.e.e	8
		2720.2.e.f	22
		2720.2.e.g	22
		2720.2.e.h	28
2720.2.f	\(\chi_{2720}(1361, \cdot)\)	2720.2.f.a	2	1
		2720.2.f.b	2
		2720.2.f.c	6
		2720.2.f.d	24
		2720.2.f.e	30
2720.2.h	\(\chi_{2720}(849, \cdot)\)	n/a	104	1
2720.2.j	\(\chi_{2720}(2449, \cdot)\)	2720.2.j.a	2	1
		2720.2.j.b	2
		2720.2.j.c	4
		2720.2.j.d	4
		2720.2.j.e	84
2720.2.l	\(\chi_{2720}(2481, \cdot)\)	2720.2.l.a	36	1
		2720.2.l.b	36
2720.2.o	\(\chi_{2720}(2209, \cdot)\)	n/a	108	1
2720.2.q	\(\chi_{2720}(1407, \cdot)\)	n/a	216	2
2720.2.s	\(\chi_{2720}(1721, \cdot)\)	None	0	2
2720.2.v	\(\chi_{2720}(1767, \cdot)\)	None	0	2
2720.2.x	\(\chi_{2720}(103, \cdot)\)	None	0	2
2720.2.z	\(\chi_{2720}(1449, \cdot)\)	None	0	2
2720.2.bb	\(\chi_{2720}(1007, \cdot)\)	n/a	208	2
2720.2.bc	\(\chi_{2720}(1543, \cdot)\)	None	0	2
2720.2.bf	\(\chi_{2720}(169, \cdot)\)	None	0	2
2720.2.bg	\(\chi_{2720}(681, \cdot)\)	None	0	2
2720.2.bj	\(\chi_{2720}(183, \cdot)\)	None	0	2
2720.2.bk	\(\chi_{2720}(1903, \cdot)\)	n/a	208	2
2720.2.bn	\(\chi_{2720}(2143, \cdot)\)	n/a	192	2
2720.2.bp	\(\chi_{2720}(769, \cdot)\)	n/a	216	2
2720.2.bq	\(\chi_{2720}(81, \cdot)\)	n/a	144	2
2720.2.bt	\(\chi_{2720}(1441, \cdot)\)	n/a	144	2
2720.2.bu	\(\chi_{2720}(1169, \cdot)\)	n/a	208	2
2720.2.bw	\(\chi_{2720}(783, \cdot)\)	n/a	192	2
2720.2.bz	\(\chi_{2720}(543, \cdot)\)	n/a	216	2
2720.2.ca	\(\chi_{2720}(1143, \cdot)\)	None	0	2
2720.2.cd	\(\chi_{2720}(441, \cdot)\)	None	0	2
2720.2.ce	\(\chi_{2720}(409, \cdot)\)	None	0	2
2720.2.ch	\(\chi_{2720}(727, \cdot)\)	None	0	2
2720.2.cj	\(\chi_{2720}(47, \cdot)\)	n/a	208	2
2720.2.ck	\(\chi_{2720}(89, \cdot)\)	None	0	2
2720.2.cm	\(\chi_{2720}(647, \cdot)\)	None	0	2
2720.2.co	\(\chi_{2720}(407, \cdot)\)	None	0	2
2720.2.cr	\(\chi_{2720}(361, \cdot)\)	None	0	2
2720.2.cs	\(\chi_{2720}(863, \cdot)\)	n/a	216	2
2720.2.cv	\(\chi_{2720}(461, \cdot)\)	n/a	1152	4
2720.2.cw	\(\chi_{2720}(467, \cdot)\)	n/a	1712	4
2720.2.cz	\(\chi_{2720}(723, \cdot)\)	n/a	1712	4
2720.2.da	\(\chi_{2720}(189, \cdot)\)	n/a	1712	4
2720.2.dd	\(\chi_{2720}(307, \cdot)\)	n/a	1536	4
2720.2.df	\(\chi_{2720}(747, \cdot)\)	n/a	1712	4
2720.2.dg	\(\chi_{2720}(149, \cdot)\)	n/a	1712	4
2720.2.dj	\(\chi_{2720}(21, \cdot)\)	n/a	1152	4
2720.2.dm	\(\chi_{2720}(43, \cdot)\)	n/a	1712	4
2720.2.dn	\(\chi_{2720}(83, \cdot)\)	n/a	1712	4
2720.2.do	\(\chi_{2720}(869, \cdot)\)	n/a	1712	4
2720.2.dq	\(\chi_{2720}(349, \cdot)\)	n/a	1712	4
2720.2.dt	\(\chi_{2720}(1141, \cdot)\)	n/a	1152	4
2720.2.dv	\(\chi_{2720}(621, \cdot)\)	n/a	1152	4
2720.2.dw	\(\chi_{2720}(563, \cdot)\)	n/a	1712	4
2720.2.dx	\(\chi_{2720}(1107, \cdot)\)	n/a	1712	4
2720.2.eb	\(\chi_{2720}(87, \cdot)\)	None	0	4
2720.2.ec	\(\chi_{2720}(161, \cdot)\)	n/a	288	4
2720.2.ef	\(\chi_{2720}(49, \cdot)\)	n/a	416	4
2720.2.eh	\(\chi_{2720}(247, \cdot)\)	None	0	4
2720.2.ej	\(\chi_{2720}(569, \cdot)\)	None	0	4
2720.2.ek	\(\chi_{2720}(281, \cdot)\)	None	0	4
2720.2.em	\(\chi_{2720}(127, \cdot)\)	n/a	432	4
2720.2.ep	\(\chi_{2720}(287, \cdot)\)	n/a	432	4
2720.2.er	\(\chi_{2720}(509, \cdot)\)	n/a	1712	4
2720.2.es	\(\chi_{2720}(101, \cdot)\)	n/a	1152	4
2720.2.eu	\(\chi_{2720}(803, \cdot)\)	n/a	1712	4
2720.2.ev	\(\chi_{2720}(523, \cdot)\)	n/a	1712	4
2720.2.fa	\(\chi_{2720}(123, \cdot)\)	n/a	1712	4
2720.2.fb	\(\chi_{2720}(667, \cdot)\)	n/a	1712	4
2720.2.fd	\(\chi_{2720}(69, \cdot)\)	n/a	1536	4
2720.2.fe	\(\chi_{2720}(341, \cdot)\)	n/a	1024	4
2720.2.fg	\(\chi_{2720}(943, \cdot)\)	n/a	416	4
2720.2.fj	\(\chi_{2720}(1103, \cdot)\)	n/a	416	4
2720.2.fl	\(\chi_{2720}(9, \cdot)\)	None	0	4
2720.2.fm	\(\chi_{2720}(121, \cdot)\)	None	0	4
2720.2.fo	\(\chi_{2720}(807, \cdot)\)	None	0	4
2720.2.fr	\(\chi_{2720}(1249, \cdot)\)	n/a	432	4
2720.2.fs	\(\chi_{2720}(1521, \cdot)\)	n/a	288	4
2720.2.fu	\(\chi_{2720}(967, \cdot)\)	None	0	4
2720.2.fx	\(\chi_{2720}(829, \cdot)\)	n/a	1712	4
2720.2.fy	\(\chi_{2720}(421, \cdot)\)	n/a	1152	4
2720.2.ga	\(\chi_{2720}(987, \cdot)\)	n/a	1536	4
2720.2.gc	\(\chi_{2720}(67, \cdot)\)	n/a	1712	4
2720.2.gf	\(\chi_{2720}(1029, \cdot)\)	n/a	1712	4
2720.2.gh	\(\chi_{2720}(427, \cdot)\)	n/a	1712	4
2720.2.gi	\(\chi_{2720}(1243, \cdot)\)	n/a	1712	4
2720.2.gk	\(\chi_{2720}(1301, \cdot)\)	n/a	1152	4
2720.2.gn	\(\chi_{2720}(231, \cdot)\)	None	0	8
2720.2.gp	\(\chi_{2720}(113, \cdot)\)	n/a	832	8
2720.2.gq	\(\chi_{2720}(513, \cdot)\)	n/a	864	8
2720.2.gs	\(\chi_{2720}(39, \cdot)\)	None	0	8
2720.2.gv	\(\chi_{2720}(91, \cdot)\)	n/a	2304	8
2720.2.gx	\(\chi_{2720}(173, \cdot)\)	n/a	3424	8
2720.2.gy	\(\chi_{2720}(453, \cdot)\)	n/a	3424	8
2720.2.ha	\(\chi_{2720}(299, \cdot)\)	n/a	3424	8
2720.2.hd	\(\chi_{2720}(313, \cdot)\)	None	0	8
2720.2.he	\(\chi_{2720}(57, \cdot)\)	None	0	8
2720.2.hg	\(\chi_{2720}(411, \cdot)\)	n/a	2304	8
2720.2.hi	\(\chi_{2720}(431, \cdot)\)	n/a	576	8
2720.2.hl	\(\chi_{2720}(31, \cdot)\)	n/a	576	8
2720.2.hn	\(\chi_{2720}(211, \cdot)\)	n/a	2304	8
2720.2.ho	\(\chi_{2720}(317, \cdot)\)	n/a	3424	8
2720.2.hr	\(\chi_{2720}(37, \cdot)\)	n/a	3424	8
2720.2.hs	\(\chi_{2720}(133, \cdot)\)	n/a	3424	8
2720.2.hv	\(\chi_{2720}(333, \cdot)\)	n/a	3424	8
2720.2.hx	\(\chi_{2720}(139, \cdot)\)	n/a	3424	8
2720.2.hz	\(\chi_{2720}(159, \cdot)\)	n/a	864	8
2720.2.ia	\(\chi_{2720}(79, \cdot)\)	n/a	832	8
2720.2.ic	\(\chi_{2720}(499, \cdot)\)	n/a	3424	8
2720.2.if	\(\chi_{2720}(377, \cdot)\)	None	0	8
2720.2.ig	\(\chi_{2720}(473, \cdot)\)	None	0	8
2720.2.ij	\(\chi_{2720}(11, \cdot)\)	n/a	2304	8
2720.2.il	\(\chi_{2720}(197, \cdot)\)	n/a	3424	8
2720.2.im	\(\chi_{2720}(533, \cdot)\)	n/a	3424	8
2720.2.io	\(\chi_{2720}(99, \cdot)\)	n/a	3424	8
2720.2.iq	\(\chi_{2720}(439, \cdot)\)	None	0	8
2720.2.is	\(\chi_{2720}(97, \cdot)\)	n/a	864	8
2720.2.iv	\(\chi_{2720}(177, \cdot)\)	n/a	832	8
2720.2.ix	\(\chi_{2720}(71, \cdot)\)	None	0	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2720))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2720)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(680))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1360))\)\(^{\oplus 2}\)