Space of modular forms of level 2240 and weight 4

• Label: 2240.4
• Level: 2240
• Weight: 4
• Dimension: 217932
• Nonzero newspaces: 56
• Sturm bound: 1179648
• Trace bound: 81

Defining parameters

Level:	\( N \)	=	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(1179648\)
Trace bound:			\(81\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2240))\).

	Total	New	Old
Modular forms	445824	219252	226572
Cusp forms	438912	217932	220980
Eisenstein series	6912	1320	5592

Trace form

217932 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 96 * q^5 - 192 * q^6 - 64 * q^7 - 160 * q^8 - 188 * q^9 - 96 * q^10 - 224 * q^11 - 64 * q^12 + 224 * q^13 - 80 * q^14 + 64 * q^15 - 192 * q^16 + 304 * q^17 - 64 * q^18 + 48 * q^19 - 96 * q^20 - 264 * q^21 + 1728 * q^22 - 56 * q^23 + 3936 * q^24 + 232 * q^25 - 352 * q^26 - 792 * q^27 - 1600 * q^28 - 1760 * q^29 - 4736 * q^30 - 1592 * q^31 - 5024 * q^32 - 3976 * q^33 - 4064 * q^34 - 568 * q^35 - 4000 * q^36 - 2144 * q^37 + 1696 * q^38 - 40 * q^39 + 3184 * q^40 + 3856 * q^41 + 6240 * q^42 + 3224 * q^43 + 3936 * q^44 + 2872 * q^45 - 192 * q^46 + 3720 * q^47 - 64 * q^48 + 1300 * q^49 - 5952 * q^50 + 17752 * q^51 - 13312 * q^52 + 1568 * q^53 - 6976 * q^54 + 1088 * q^55 + 544 * q^56 - 4080 * q^57 + 9440 * q^58 - 17888 * q^59 + 9696 * q^60 - 4512 * q^61 + 11904 * q^62 - 12672 * q^63 + 24032 * q^64 + 3572 * q^65 + 21952 * q^66 - 16752 * q^67 + 8192 * q^68 + 3344 * q^69 + 1896 * q^70 - 3056 * q^71 - 2656 * q^72 - 720 * q^73 - 10592 * q^74 + 948 * q^75 - 24000 * q^76 - 840 * q^77 - 8128 * q^78 + 27608 * q^79 + 8432 * q^80 + 7876 * q^81 + 27776 * q^82 - 528 * q^83 + 8208 * q^84 - 6336 * q^85 - 2272 * q^86 - 5208 * q^87 - 12544 * q^88 - 12944 * q^89 - 18816 * q^90 + 4776 * q^91 - 50624 * q^92 + 8384 * q^93 - 35776 * q^94 + 13188 * q^95 - 51872 * q^96 - 3920 * q^97 - 24288 * q^98 + 3368 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2240))\)

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
2240.4.a	\(\chi_{2240}(1, \cdot)\)	2240.4.a.a	1	1
		2240.4.a.b	1
		2240.4.a.c	1
		2240.4.a.d	1
		2240.4.a.e	1
		2240.4.a.f	1
		2240.4.a.g	1
		2240.4.a.h	1
		2240.4.a.i	1
		2240.4.a.j	1
		2240.4.a.k	1
		2240.4.a.l	1
		2240.4.a.m	1
		2240.4.a.n	1
		2240.4.a.o	1
		2240.4.a.p	1
		2240.4.a.q	1
		2240.4.a.r	1
		2240.4.a.s	1
		2240.4.a.t	1
		2240.4.a.u	1
		2240.4.a.v	1
		2240.4.a.w	1
		2240.4.a.x	1
		2240.4.a.y	1
		2240.4.a.z	1
		2240.4.a.ba	1
		2240.4.a.bb	1
		2240.4.a.bc	1
		2240.4.a.bd	1
		2240.4.a.be	1
		2240.4.a.bf	1
		2240.4.a.bg	1
		2240.4.a.bh	1
		2240.4.a.bi	1
		2240.4.a.bj	1
		2240.4.a.bk	1
		2240.4.a.bl	1
		2240.4.a.bm	2
		2240.4.a.bn	2
		2240.4.a.bo	2
		2240.4.a.bp	2
		2240.4.a.bq	3
		2240.4.a.br	3
		2240.4.a.bs	3
		2240.4.a.bt	3
		2240.4.a.bu	3
		2240.4.a.bv	3
		2240.4.a.bw	3
		2240.4.a.bx	3
		2240.4.a.by	3
		2240.4.a.bz	3
		2240.4.a.ca	4
		2240.4.a.cb	4
		2240.4.a.cc	4
		2240.4.a.cd	4
		2240.4.a.ce	4
		2240.4.a.cf	4
		2240.4.a.cg	4
		2240.4.a.ch	4
		2240.4.a.ci	4
		2240.4.a.cj	4
		2240.4.a.ck	4
		2240.4.a.cl	4
2240.4.a.cm	5
2240.4.a.cn	5
2240.4.a.co	5
2240.4.a.cp	5
2240.4.b	\(\chi_{2240}(1121, \cdot)\)	n/a	144	1
2240.4.e	\(\chi_{2240}(2239, \cdot)\)	n/a	284	1
2240.4.g	\(\chi_{2240}(449, \cdot)\)	n/a	216	1
2240.4.h	\(\chi_{2240}(671, \cdot)\)	n/a	192	1
2240.4.k	\(\chi_{2240}(1791, \cdot)\)	n/a	192	1
2240.4.l	\(\chi_{2240}(1569, \cdot)\)	n/a	216	1
2240.4.n	\(\chi_{2240}(1119, \cdot)\)	n/a	288	1
2240.4.q	\(\chi_{2240}(641, \cdot)\)	n/a	384	2
2240.4.r	\(\chi_{2240}(433, \cdot)\)	n/a	568	2
2240.4.t	\(\chi_{2240}(463, \cdot)\)	n/a	432	2
2240.4.w	\(\chi_{2240}(97, \cdot)\)	n/a	576	2
2240.4.x	\(\chi_{2240}(127, \cdot)\)	n/a	432	2
2240.4.bb	\(\chi_{2240}(1009, \cdot)\)	n/a	432	2
2240.4.bc	\(\chi_{2240}(111, \cdot)\)	n/a	384	2
2240.4.bd	\(\chi_{2240}(561, \cdot)\)	n/a	288	2
2240.4.be	\(\chi_{2240}(559, \cdot)\)	n/a	568	2
2240.4.bi	\(\chi_{2240}(1247, \cdot)\)	n/a	432	2
2240.4.bj	\(\chi_{2240}(1217, \cdot)\)	n/a	568	2
2240.4.bl	\(\chi_{2240}(1583, \cdot)\)	n/a	432	2
2240.4.bn	\(\chi_{2240}(1553, \cdot)\)	n/a	568	2
2240.4.bq	\(\chi_{2240}(159, \cdot)\)	n/a	576	2
2240.4.bs	\(\chi_{2240}(831, \cdot)\)	n/a	384	2
2240.4.bv	\(\chi_{2240}(289, \cdot)\)	n/a	576	2
2240.4.bw	\(\chi_{2240}(1089, \cdot)\)	n/a	568	2
2240.4.bz	\(\chi_{2240}(31, \cdot)\)	n/a	384	2
2240.4.cb	\(\chi_{2240}(1761, \cdot)\)	n/a	384	2
2240.4.cc	\(\chi_{2240}(1279, \cdot)\)	n/a	568	2
2240.4.cg	\(\chi_{2240}(281, \cdot)\)	None	0	4
2240.4.ch	\(\chi_{2240}(279, \cdot)\)	None	0	4
2240.4.ci	\(\chi_{2240}(377, \cdot)\)	None	0	4
2240.4.cj	\(\chi_{2240}(407, \cdot)\)	None	0	4
2240.4.cm	\(\chi_{2240}(183, \cdot)\)	None	0	4
2240.4.cn	\(\chi_{2240}(153, \cdot)\)	None	0	4
2240.4.cs	\(\chi_{2240}(391, \cdot)\)	None	0	4
2240.4.ct	\(\chi_{2240}(169, \cdot)\)	None	0	4
2240.4.cv	\(\chi_{2240}(207, \cdot)\)	n/a	1136	4
2240.4.cx	\(\chi_{2240}(593, \cdot)\)	n/a	1136	4
2240.4.cy	\(\chi_{2240}(257, \cdot)\)	n/a	1136	4
2240.4.db	\(\chi_{2240}(543, \cdot)\)	n/a	1152	4
2240.4.de	\(\chi_{2240}(719, \cdot)\)	n/a	1136	4
2240.4.df	\(\chi_{2240}(81, \cdot)\)	n/a	768	4
2240.4.dg	\(\chi_{2240}(271, \cdot)\)	n/a	768	4
2240.4.dh	\(\chi_{2240}(529, \cdot)\)	n/a	1136	4
2240.4.dk	\(\chi_{2240}(767, \cdot)\)	n/a	1136	4
2240.4.dn	\(\chi_{2240}(33, \cdot)\)	n/a	1152	4
2240.4.dp	\(\chi_{2240}(17, \cdot)\)	n/a	1136	4
2240.4.dr	\(\chi_{2240}(1103, \cdot)\)	n/a	1136	4
2240.4.du	\(\chi_{2240}(13, \cdot)\)	n/a	9184	8
2240.4.dv	\(\chi_{2240}(43, \cdot)\)	n/a	6912	8
2240.4.dw	\(\chi_{2240}(139, \cdot)\)	n/a	9184	8
2240.4.dx	\(\chi_{2240}(141, \cdot)\)	n/a	4608	8
2240.4.dy	\(\chi_{2240}(251, \cdot)\)	n/a	6144	8
2240.4.dz	\(\chi_{2240}(29, \cdot)\)	n/a	6912	8
2240.4.eg	\(\chi_{2240}(267, \cdot)\)	n/a	6912	8
2240.4.eh	\(\chi_{2240}(237, \cdot)\)	n/a	9184	8
2240.4.ei	\(\chi_{2240}(9, \cdot)\)	None	0	8
2240.4.ej	\(\chi_{2240}(311, \cdot)\)	None	0	8
2240.4.eo	\(\chi_{2240}(23, \cdot)\)	None	0	8
2240.4.ep	\(\chi_{2240}(297, \cdot)\)	None	0	8
2240.4.es	\(\chi_{2240}(73, \cdot)\)	None	0	8
2240.4.et	\(\chi_{2240}(247, \cdot)\)	None	0	8
2240.4.eu	\(\chi_{2240}(199, \cdot)\)	None	0	8
2240.4.ev	\(\chi_{2240}(121, \cdot)\)	None	0	8
2240.4.ey	\(\chi_{2240}(157, \cdot)\)	n/a	18368	16
2240.4.ez	\(\chi_{2240}(107, \cdot)\)	n/a	18368	16
2240.4.fg	\(\chi_{2240}(109, \cdot)\)	n/a	18368	16
2240.4.fh	\(\chi_{2240}(131, \cdot)\)	n/a	12288	16
2240.4.fi	\(\chi_{2240}(221, \cdot)\)	n/a	12288	16
2240.4.fj	\(\chi_{2240}(19, \cdot)\)	n/a	18368	16
2240.4.fk	\(\chi_{2240}(67, \cdot)\)	n/a	18368	16
2240.4.fl	\(\chi_{2240}(117, \cdot)\)	n/a	18368	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2240))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2240)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1120))\)\(^{\oplus 2}\)