Space of modular forms of level 2160 and weight 4

• Label: 2160.4
• Level: 2160
• Weight: 4
• Dimension: 151632
• Nonzero newspaces: 42
• Sturm bound: 995328
• Trace bound: 31

Defining parameters

Level:	\( N \)	=	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(995328\)
Trace bound:			\(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2160))\).

	Total	New	Old
Modular forms	376608	152496	224112
Cusp forms	369888	151632	218256
Eisenstein series	6720	864	5856

Trace form

151632 * q - 32 * q^2 - 36 * q^3 - 56 * q^4 - 59 * q^5 - 144 * q^6 - 6 * q^7 - 32 * q^8 - 12 * q^9 - 84 * q^10 - 206 * q^11 - 48 * q^12 - 142 * q^13 - 96 * q^14 - 54 * q^15 - 696 * q^16 - 234 * q^17 - 48 * q^18 + 162 * q^19 + 260 * q^20 - 180 * q^21 + 952 * q^22 + 242 * q^23 - 48 * q^24 + 315 * q^25 + 992 * q^26 - 1368 * q^27 + 16 * q^28 - 826 * q^29 - 72 * q^30 + 270 * q^31 - 1992 * q^32 + 1284 * q^33 - 1448 * q^34 + 1319 * q^35 - 144 * q^36 + 1538 * q^37 + 2376 * q^38 + 1620 * q^39 + 204 * q^40 + 418 * q^41 - 48 * q^42 + 1194 * q^43 - 3112 * q^44 - 1410 * q^45 - 2920 * q^46 - 2302 * q^47 - 48 * q^48 - 1628 * q^49 - 2212 * q^50 + 54 * q^51 - 1784 * q^52 + 784 * q^53 - 48 * q^54 + 1150 * q^55 + 15624 * q^56 + 6498 * q^57 + 18184 * q^58 + 2102 * q^59 + 7248 * q^60 + 4614 * q^61 + 12304 * q^62 + 24 * q^63 - 2216 * q^64 - 3105 * q^65 - 14904 * q^66 - 2478 * q^67 - 30200 * q^68 - 12540 * q^69 - 13332 * q^70 - 9962 * q^71 - 23904 * q^72 - 8174 * q^73 - 36432 * q^74 - 2532 * q^75 - 19752 * q^76 - 17214 * q^77 - 9096 * q^78 + 1482 * q^79 + 4892 * q^80 + 3324 * q^81 + 12448 * q^82 + 6746 * q^83 + 22392 * q^84 + 5093 * q^85 + 54984 * q^86 + 6048 * q^87 + 22552 * q^88 + 25474 * q^89 + 8676 * q^90 - 6230 * q^91 - 12136 * q^92 + 14772 * q^93 - 9112 * q^94 + 817 * q^95 - 144 * q^96 + 2802 * q^97 - 9328 * q^98 - 7596 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2160))\)

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
2160.4.a	\(\chi_{2160}(1, \cdot)\)	2160.4.a.a	1	1
		2160.4.a.b	1
		2160.4.a.c	1
		2160.4.a.d	1
		2160.4.a.e	1
		2160.4.a.f	1
		2160.4.a.g	1
		2160.4.a.h	1
		2160.4.a.i	1
		2160.4.a.j	1
		2160.4.a.k	1
		2160.4.a.l	1
		2160.4.a.m	1
		2160.4.a.n	1
		2160.4.a.o	1
		2160.4.a.p	1
		2160.4.a.q	1
		2160.4.a.r	1
		2160.4.a.s	1
		2160.4.a.t	1
		2160.4.a.u	2
		2160.4.a.v	2
		2160.4.a.w	2
		2160.4.a.x	2
		2160.4.a.y	2
		2160.4.a.z	2
		2160.4.a.ba	2
		2160.4.a.bb	2
		2160.4.a.bc	2
		2160.4.a.bd	2
		2160.4.a.be	3
		2160.4.a.bf	3
		2160.4.a.bg	3
		2160.4.a.bh	3
		2160.4.a.bi	3
		2160.4.a.bj	3
		2160.4.a.bk	3
		2160.4.a.bl	3
		2160.4.a.bm	3
		2160.4.a.bn	3
		2160.4.a.bo	3
		2160.4.a.bp	3
		2160.4.a.bq	3
		2160.4.a.br	3
		2160.4.a.bs	3
		2160.4.a.bt	3
		2160.4.a.bu	4
		2160.4.a.bv	4
2160.4.b	\(\chi_{2160}(1511, \cdot)\)	None	0	1
2160.4.d	\(\chi_{2160}(649, \cdot)\)	None	0	1
2160.4.f	\(\chi_{2160}(1729, \cdot)\)	n/a	144	1
2160.4.h	\(\chi_{2160}(431, \cdot)\)	2160.4.h.a	4	1
		2160.4.h.b	4
		2160.4.h.c	12
		2160.4.h.d	12
		2160.4.h.e	12
		2160.4.h.f	16
		2160.4.h.g	16
		2160.4.h.h	20
2160.4.k	\(\chi_{2160}(1081, \cdot)\)	None	0	1
2160.4.m	\(\chi_{2160}(1079, \cdot)\)	None	0	1
2160.4.o	\(\chi_{2160}(2159, \cdot)\)	n/a	144	1
2160.4.q	\(\chi_{2160}(721, \cdot)\)	n/a	144	2
2160.4.t	\(\chi_{2160}(541, \cdot)\)	n/a	768	2
2160.4.u	\(\chi_{2160}(539, \cdot)\)	n/a	1152	2
2160.4.w	\(\chi_{2160}(593, \cdot)\)	n/a	288	2
2160.4.x	\(\chi_{2160}(703, \cdot)\)	n/a	288	2
2160.4.z	\(\chi_{2160}(163, \cdot)\)	n/a	1152	2
2160.4.bc	\(\chi_{2160}(917, \cdot)\)	n/a	1152	2
2160.4.bd	\(\chi_{2160}(1027, \cdot)\)	n/a	1152	2
2160.4.bg	\(\chi_{2160}(53, \cdot)\)	n/a	1152	2
2160.4.bi	\(\chi_{2160}(487, \cdot)\)	None	0	2
2160.4.bj	\(\chi_{2160}(377, \cdot)\)	None	0	2
2160.4.bl	\(\chi_{2160}(971, \cdot)\)	n/a	768	2
2160.4.bm	\(\chi_{2160}(109, \cdot)\)	n/a	1152	2
2160.4.br	\(\chi_{2160}(719, \cdot)\)	n/a	216	2
2160.4.bt	\(\chi_{2160}(359, \cdot)\)	None	0	2
2160.4.bv	\(\chi_{2160}(361, \cdot)\)	None	0	2
2160.4.bw	\(\chi_{2160}(1151, \cdot)\)	n/a	144	2
2160.4.by	\(\chi_{2160}(289, \cdot)\)	n/a	212	2
2160.4.ca	\(\chi_{2160}(1369, \cdot)\)	None	0	2
2160.4.cc	\(\chi_{2160}(71, \cdot)\)	None	0	2
2160.4.ce	\(\chi_{2160}(241, \cdot)\)	n/a	1296	6
2160.4.cf	\(\chi_{2160}(469, \cdot)\)	n/a	1712	4
2160.4.cg	\(\chi_{2160}(251, \cdot)\)	n/a	1152	4
2160.4.cj	\(\chi_{2160}(343, \cdot)\)	None	0	4
2160.4.cm	\(\chi_{2160}(233, \cdot)\)	None	0	4
2160.4.cn	\(\chi_{2160}(557, \cdot)\)	n/a	1712	4
2160.4.cq	\(\chi_{2160}(307, \cdot)\)	n/a	1712	4
2160.4.cr	\(\chi_{2160}(197, \cdot)\)	n/a	1712	4
2160.4.cu	\(\chi_{2160}(667, \cdot)\)	n/a	1712	4
2160.4.cv	\(\chi_{2160}(17, \cdot)\)	n/a	424	4
2160.4.cy	\(\chi_{2160}(127, \cdot)\)	n/a	432	4
2160.4.db	\(\chi_{2160}(179, \cdot)\)	n/a	1712	4
2160.4.dc	\(\chi_{2160}(181, \cdot)\)	n/a	1152	4
2160.4.dd	\(\chi_{2160}(119, \cdot)\)	None	0	6
2160.4.di	\(\chi_{2160}(121, \cdot)\)	None	0	6
2160.4.dj	\(\chi_{2160}(239, \cdot)\)	n/a	1944	6
2160.4.dm	\(\chi_{2160}(49, \cdot)\)	n/a	1932	6
2160.4.dn	\(\chi_{2160}(311, \cdot)\)	None	0	6
2160.4.do	\(\chi_{2160}(191, \cdot)\)	n/a	1296	6
2160.4.dp	\(\chi_{2160}(169, \cdot)\)	None	0	6
2160.4.du	\(\chi_{2160}(59, \cdot)\)	n/a	15504	12
2160.4.dv	\(\chi_{2160}(61, \cdot)\)	n/a	10368	12
2160.4.dy	\(\chi_{2160}(137, \cdot)\)	None	0	12
2160.4.dz	\(\chi_{2160}(223, \cdot)\)	n/a	3888	12
2160.4.ea	\(\chi_{2160}(43, \cdot)\)	n/a	15504	12
2160.4.ec	\(\chi_{2160}(77, \cdot)\)	n/a	15504	12
2160.4.ee	\(\chi_{2160}(173, \cdot)\)	n/a	15504	12
2160.4.eg	\(\chi_{2160}(187, \cdot)\)	n/a	15504	12
2160.4.ek	\(\chi_{2160}(113, \cdot)\)	n/a	3864	12
2160.4.el	\(\chi_{2160}(7, \cdot)\)	None	0	12
2160.4.eo	\(\chi_{2160}(229, \cdot)\)	n/a	15504	12
2160.4.ep	\(\chi_{2160}(11, \cdot)\)	n/a	10368	12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2160))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2160)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 2}\)