Space of modular forms of level 2240 and weight 2

• Label: 2240.2
• Level: 2240
• Weight: 2
• Dimension: 72204
• Nonzero newspaces: 56
• Sturm bound: 589824
• Trace bound: 81

Defining parameters

Level:	\( N \)	=	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(589824\)
Trace bound:			\(81\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2240))\).

	Total	New	Old
Modular forms	150912	73524	77388
Cusp forms	144001	72204	71797
Eisenstein series	6911	1320	5591

Trace form

72204 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 96 * q^5 - 192 * q^6 - 64 * q^7 - 160 * q^8 - 92 * q^9 - 96 * q^10 - 160 * q^11 - 64 * q^12 - 96 * q^13 - 80 * q^14 - 192 * q^15 - 192 * q^16 - 144 * q^17 - 64 * q^18 - 80 * q^19 - 96 * q^20 - 232 * q^21 - 128 * q^22 - 56 * q^23 + 96 * q^24 - 88 * q^25 - 32 * q^26 - 24 * q^27 - 96 * q^29 + 64 * q^30 - 56 * q^31 + 96 * q^32 + 56 * q^33 + 96 * q^34 - 88 * q^35 - 160 * q^36 - 32 * q^37 + 96 * q^38 - 40 * q^39 - 16 * q^40 - 240 * q^41 - 168 * q^43 - 32 * q^44 - 104 * q^45 - 192 * q^46 - 120 * q^47 - 64 * q^48 - 172 * q^49 - 288 * q^50 - 40 * q^51 - 256 * q^52 - 160 * q^53 - 320 * q^54 + 64 * q^55 - 352 * q^56 - 176 * q^57 - 352 * q^58 + 224 * q^59 - 288 * q^60 - 224 * q^61 - 192 * q^62 + 128 * q^63 - 544 * q^64 - 204 * q^65 - 512 * q^66 + 400 * q^67 - 256 * q^68 + 80 * q^69 - 216 * q^70 + 16 * q^71 - 352 * q^72 + 48 * q^73 - 288 * q^74 + 244 * q^75 - 448 * q^76 + 24 * q^77 - 256 * q^78 + 216 * q^79 - 16 * q^80 + 4 * q^81 + 256 * q^82 + 112 * q^83 + 144 * q^84 - 32 * q^85 + 224 * q^86 + 168 * q^87 + 256 * q^88 + 240 * q^89 + 192 * q^90 + 40 * q^91 + 448 * q^92 + 384 * q^93 + 320 * q^94 + 132 * q^95 + 352 * q^96 + 368 * q^97 + 192 * q^98 + 360 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2240))\)

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
2240.2.a	\(\chi_{2240}(1, \cdot)\)	2240.2.a.a	1	1
		2240.2.a.b	1
		2240.2.a.c	1
		2240.2.a.d	1
		2240.2.a.e	1
		2240.2.a.f	1
		2240.2.a.g	1
		2240.2.a.h	1
		2240.2.a.i	1
		2240.2.a.j	1
		2240.2.a.k	1
		2240.2.a.l	1
		2240.2.a.m	1
		2240.2.a.n	1
		2240.2.a.o	1
		2240.2.a.p	1
		2240.2.a.q	1
		2240.2.a.r	1
		2240.2.a.s	1
		2240.2.a.t	1
		2240.2.a.u	1
		2240.2.a.v	1
		2240.2.a.w	1
		2240.2.a.x	1
		2240.2.a.y	1
		2240.2.a.z	1
		2240.2.a.ba	1
		2240.2.a.bb	1
		2240.2.a.bc	2
		2240.2.a.bd	2
		2240.2.a.be	2
		2240.2.a.bf	2
		2240.2.a.bg	2
		2240.2.a.bh	2
		2240.2.a.bi	2
		2240.2.a.bj	2
		2240.2.a.bk	2
		2240.2.a.bl	2
2240.2.b	\(\chi_{2240}(1121, \cdot)\)	2240.2.b.a	2	1
		2240.2.b.b	2
		2240.2.b.c	4
		2240.2.b.d	4
		2240.2.b.e	6
		2240.2.b.f	6
		2240.2.b.g	12
		2240.2.b.h	12
2240.2.e	\(\chi_{2240}(2239, \cdot)\)	2240.2.e.a	4	1
		2240.2.e.b	4
		2240.2.e.c	4
		2240.2.e.d	8
		2240.2.e.e	8
		2240.2.e.f	16
		2240.2.e.g	48
2240.2.g	\(\chi_{2240}(449, \cdot)\)	2240.2.g.a	2	1
		2240.2.g.b	2
		2240.2.g.c	2
		2240.2.g.d	2
		2240.2.g.e	2
		2240.2.g.f	2
		2240.2.g.g	2
		2240.2.g.h	2
		2240.2.g.i	4
		2240.2.g.j	4
		2240.2.g.k	4
		2240.2.g.l	6
		2240.2.g.m	6
		2240.2.g.n	10
		2240.2.g.o	10
		2240.2.g.p	12
2240.2.h	\(\chi_{2240}(671, \cdot)\)	2240.2.h.a	4	1
		2240.2.h.b	4
		2240.2.h.c	4
		2240.2.h.d	4
		2240.2.h.e	24
		2240.2.h.f	24
2240.2.k	\(\chi_{2240}(1791, \cdot)\)	2240.2.k.a	4	1
		2240.2.k.b	4
		2240.2.k.c	8
		2240.2.k.d	8
		2240.2.k.e	8
		2240.2.k.f	16
		2240.2.k.g	16
2240.2.l	\(\chi_{2240}(1569, \cdot)\)	2240.2.l.a	12	1
		2240.2.l.b	12
		2240.2.l.c	24
		2240.2.l.d	24
2240.2.n	\(\chi_{2240}(1119, \cdot)\)	2240.2.n.a	8	1
		2240.2.n.b	8
		2240.2.n.c	8
		2240.2.n.d	8
		2240.2.n.e	8
		2240.2.n.f	8
		2240.2.n.g	8
		2240.2.n.h	8
		2240.2.n.i	16
		2240.2.n.j	16
2240.2.q	\(\chi_{2240}(641, \cdot)\)	n/a	128	2
2240.2.r	\(\chi_{2240}(433, \cdot)\)	n/a	184	2
2240.2.t	\(\chi_{2240}(463, \cdot)\)	n/a	144	2
2240.2.w	\(\chi_{2240}(97, \cdot)\)	n/a	192	2
2240.2.x	\(\chi_{2240}(127, \cdot)\)	n/a	144	2
2240.2.bb	\(\chi_{2240}(1009, \cdot)\)	n/a	144	2
2240.2.bc	\(\chi_{2240}(111, \cdot)\)	n/a	128	2
2240.2.bd	\(\chi_{2240}(561, \cdot)\)	2240.2.bd.a	44	2
		2240.2.bd.b	52
2240.2.be	\(\chi_{2240}(559, \cdot)\)	n/a	184	2
2240.2.bi	\(\chi_{2240}(1247, \cdot)\)	n/a	144	2
2240.2.bj	\(\chi_{2240}(1217, \cdot)\)	n/a	184	2
2240.2.bl	\(\chi_{2240}(1583, \cdot)\)	n/a	144	2
2240.2.bn	\(\chi_{2240}(1553, \cdot)\)	n/a	184	2
2240.2.bq	\(\chi_{2240}(159, \cdot)\)	n/a	192	2
2240.2.bs	\(\chi_{2240}(831, \cdot)\)	n/a	128	2
2240.2.bv	\(\chi_{2240}(289, \cdot)\)	n/a	192	2
2240.2.bw	\(\chi_{2240}(1089, \cdot)\)	n/a	184	2
2240.2.bz	\(\chi_{2240}(31, \cdot)\)	n/a	128	2
2240.2.cb	\(\chi_{2240}(1761, \cdot)\)	n/a	128	2
2240.2.cc	\(\chi_{2240}(1279, \cdot)\)	n/a	184	2
2240.2.cg	\(\chi_{2240}(281, \cdot)\)	None	0	4
2240.2.ch	\(\chi_{2240}(279, \cdot)\)	None	0	4
2240.2.ci	\(\chi_{2240}(377, \cdot)\)	None	0	4
2240.2.cj	\(\chi_{2240}(407, \cdot)\)	None	0	4
2240.2.cm	\(\chi_{2240}(183, \cdot)\)	None	0	4
2240.2.cn	\(\chi_{2240}(153, \cdot)\)	None	0	4
2240.2.cs	\(\chi_{2240}(391, \cdot)\)	None	0	4
2240.2.ct	\(\chi_{2240}(169, \cdot)\)	None	0	4
2240.2.cv	\(\chi_{2240}(207, \cdot)\)	n/a	368	4
2240.2.cx	\(\chi_{2240}(593, \cdot)\)	n/a	368	4
2240.2.cy	\(\chi_{2240}(257, \cdot)\)	n/a	368	4
2240.2.db	\(\chi_{2240}(543, \cdot)\)	n/a	384	4
2240.2.de	\(\chi_{2240}(719, \cdot)\)	n/a	368	4
2240.2.df	\(\chi_{2240}(81, \cdot)\)	n/a	256	4
2240.2.dg	\(\chi_{2240}(271, \cdot)\)	n/a	256	4
2240.2.dh	\(\chi_{2240}(529, \cdot)\)	n/a	368	4
2240.2.dk	\(\chi_{2240}(767, \cdot)\)	n/a	368	4
2240.2.dn	\(\chi_{2240}(33, \cdot)\)	n/a	384	4
2240.2.dp	\(\chi_{2240}(17, \cdot)\)	n/a	368	4
2240.2.dr	\(\chi_{2240}(1103, \cdot)\)	n/a	368	4
2240.2.du	\(\chi_{2240}(13, \cdot)\)	n/a	3040	8
2240.2.dv	\(\chi_{2240}(43, \cdot)\)	n/a	2304	8
2240.2.dw	\(\chi_{2240}(139, \cdot)\)	n/a	3040	8
2240.2.dx	\(\chi_{2240}(141, \cdot)\)	n/a	1536	8
2240.2.dy	\(\chi_{2240}(251, \cdot)\)	n/a	2048	8
2240.2.dz	\(\chi_{2240}(29, \cdot)\)	n/a	2304	8
2240.2.eg	\(\chi_{2240}(267, \cdot)\)	n/a	2304	8
2240.2.eh	\(\chi_{2240}(237, \cdot)\)	n/a	3040	8
2240.2.ei	\(\chi_{2240}(9, \cdot)\)	None	0	8
2240.2.ej	\(\chi_{2240}(311, \cdot)\)	None	0	8
2240.2.eo	\(\chi_{2240}(23, \cdot)\)	None	0	8
2240.2.ep	\(\chi_{2240}(297, \cdot)\)	None	0	8
2240.2.es	\(\chi_{2240}(73, \cdot)\)	None	0	8
2240.2.et	\(\chi_{2240}(247, \cdot)\)	None	0	8
2240.2.eu	\(\chi_{2240}(199, \cdot)\)	None	0	8
2240.2.ev	\(\chi_{2240}(121, \cdot)\)	None	0	8
2240.2.ey	\(\chi_{2240}(157, \cdot)\)	n/a	6080	16
2240.2.ez	\(\chi_{2240}(107, \cdot)\)	n/a	6080	16
2240.2.fg	\(\chi_{2240}(109, \cdot)\)	n/a	6080	16
2240.2.fh	\(\chi_{2240}(131, \cdot)\)	n/a	4096	16
2240.2.fi	\(\chi_{2240}(221, \cdot)\)	n/a	4096	16
2240.2.fj	\(\chi_{2240}(19, \cdot)\)	n/a	6080	16
2240.2.fk	\(\chi_{2240}(67, \cdot)\)	n/a	6080	16
2240.2.fl	\(\chi_{2240}(117, \cdot)\)	n/a	6080	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2240))\) into lower level spaces

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