Space of modular forms of level 1120 and weight 2

• Label: 1120.2
• Level: 1120
• Weight: 2
• Dimension: 17916
• Nonzero newspaces: 40
• Sturm bound: 147456
• Trace bound: 21

Defining parameters

Level:	\( N \)	=	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(147456\)
Trace bound:			\(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1120))\).

	Total	New	Old
Modular forms	38400	18516	19884
Cusp forms	35329	17916	17413
Eisenstein series	3071	600	2471

Trace form

17916 * q - 32 * q^2 - 28 * q^3 - 32 * q^4 - 52 * q^5 - 96 * q^6 - 32 * q^7 - 80 * q^8 - 52 * q^9 - 32 * q^10 - 76 * q^11 + 32 * q^12 - 8 * q^13 - 8 * q^14 - 84 * q^15 - 16 * q^16 + 48 * q^18 - 20 * q^19 - 16 * q^20 - 120 * q^21 - 32 * q^22 + 4 * q^23 - 80 * q^24 - 80 * q^25 - 176 * q^26 + 104 * q^27 - 80 * q^28 - 104 * q^29 - 112 * q^30 + 36 * q^31 - 112 * q^32 - 8 * q^33 - 80 * q^34 + 2 * q^35 - 352 * q^36 + 40 * q^37 + 160 * q^39 - 24 * q^40 - 32 * q^41 + 56 * q^43 + 128 * q^44 + 116 * q^45 + 32 * q^46 + 108 * q^47 + 176 * q^48 + 84 * q^49 - 40 * q^50 + 60 * q^51 + 200 * q^53 + 16 * q^54 - 20 * q^55 - 96 * q^56 + 32 * q^57 - 48 * q^58 - 52 * q^59 - 184 * q^60 + 88 * q^61 - 112 * q^62 - 16 * q^63 - 320 * q^64 - 156 * q^65 - 448 * q^66 - 164 * q^67 - 176 * q^68 - 216 * q^70 - 352 * q^71 - 416 * q^72 - 192 * q^73 - 320 * q^74 - 214 * q^75 - 352 * q^76 - 104 * q^77 - 528 * q^78 - 132 * q^79 - 376 * q^80 - 332 * q^81 - 352 * q^82 + 64 * q^83 - 304 * q^84 - 280 * q^85 - 432 * q^86 + 144 * q^87 - 368 * q^88 - 128 * q^89 - 648 * q^90 - 112 * q^91 - 560 * q^92 - 368 * q^93 - 496 * q^94 + 38 * q^95 - 816 * q^96 - 256 * q^97 - 464 * q^98 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1120))\)

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
1120.2.a	\(\chi_{1120}(1, \cdot)\)	1120.2.a.a	1	1
		1120.2.a.b	1
		1120.2.a.c	1
		1120.2.a.d	1
		1120.2.a.e	1
		1120.2.a.f	1
		1120.2.a.g	1
		1120.2.a.h	1
		1120.2.a.i	1
		1120.2.a.j	1
		1120.2.a.k	1
		1120.2.a.l	1
		1120.2.a.m	1
		1120.2.a.n	1
		1120.2.a.o	1
		1120.2.a.p	1
		1120.2.a.q	2
		1120.2.a.r	2
		1120.2.a.s	2
		1120.2.a.t	2
1120.2.b	\(\chi_{1120}(561, \cdot)\)	1120.2.b.a	2	1
		1120.2.b.b	2
		1120.2.b.c	8
		1120.2.b.d	12
1120.2.e	\(\chi_{1120}(1119, \cdot)\)	1120.2.e.a	48	1
1120.2.g	\(\chi_{1120}(449, \cdot)\)	1120.2.g.a	4	1
		1120.2.g.b	10
		1120.2.g.c	10
		1120.2.g.d	12
1120.2.h	\(\chi_{1120}(111, \cdot)\)	1120.2.h.a	16	1
		1120.2.h.b	16
1120.2.k	\(\chi_{1120}(671, \cdot)\)	1120.2.k.a	16	1
		1120.2.k.b	16
1120.2.l	\(\chi_{1120}(1009, \cdot)\)	1120.2.l.a	36	1
1120.2.n	\(\chi_{1120}(559, \cdot)\)	1120.2.n.a	4	1
		1120.2.n.b	40
1120.2.q	\(\chi_{1120}(641, \cdot)\)	1120.2.q.a	2	2
		1120.2.q.b	2
		1120.2.q.c	2
		1120.2.q.d	2
		1120.2.q.e	4
		1120.2.q.f	4
		1120.2.q.g	8
		1120.2.q.h	8
		1120.2.q.i	10
		1120.2.q.j	10
		1120.2.q.k	12
1120.2.r	\(\chi_{1120}(153, \cdot)\)	None	0	2
1120.2.t	\(\chi_{1120}(407, \cdot)\)	None	0	2
1120.2.w	\(\chi_{1120}(433, \cdot)\)	1120.2.w.a	8	2
		1120.2.w.b	8
		1120.2.w.c	72
1120.2.x	\(\chi_{1120}(127, \cdot)\)	1120.2.x.a	4	2
		1120.2.x.b	4
		1120.2.x.c	12
		1120.2.x.d	12
		1120.2.x.e	20
		1120.2.x.f	20
1120.2.bb	\(\chi_{1120}(169, \cdot)\)	None	0	2
1120.2.bc	\(\chi_{1120}(391, \cdot)\)	None	0	2
1120.2.bd	\(\chi_{1120}(281, \cdot)\)	None	0	2
1120.2.be	\(\chi_{1120}(279, \cdot)\)	None	0	2
1120.2.bi	\(\chi_{1120}(463, \cdot)\)	1120.2.bi.a	72	2
1120.2.bj	\(\chi_{1120}(97, \cdot)\)	1120.2.bj.a	8	2
		1120.2.bj.b	8
		1120.2.bj.c	32
		1120.2.bj.d	48
1120.2.bl	\(\chi_{1120}(183, \cdot)\)	None	0	2
1120.2.bn	\(\chi_{1120}(377, \cdot)\)	None	0	2
1120.2.bq	\(\chi_{1120}(719, \cdot)\)	1120.2.bq.a	8	2
		1120.2.bq.b	80
1120.2.bs	\(\chi_{1120}(31, \cdot)\)	1120.2.bs.a	32	2
		1120.2.bs.b	32
1120.2.bv	\(\chi_{1120}(529, \cdot)\)	1120.2.bv.a	88	2
1120.2.bw	\(\chi_{1120}(289, \cdot)\)	1120.2.bw.a	4	2
		1120.2.bw.b	4
		1120.2.bw.c	8
		1120.2.bw.d	8
		1120.2.bw.e	8
		1120.2.bw.f	8
		1120.2.bw.g	16
		1120.2.bw.h	40
1120.2.bz	\(\chi_{1120}(271, \cdot)\)	1120.2.bz.a	4	2
		1120.2.bz.b	4
		1120.2.bz.c	4
		1120.2.bz.d	4
		1120.2.bz.e	24
		1120.2.bz.f	24
1120.2.cb	\(\chi_{1120}(81, \cdot)\)	1120.2.cb.a	4	2
		1120.2.cb.b	60
1120.2.cc	\(\chi_{1120}(159, \cdot)\)	1120.2.cc.a	8	2
		1120.2.cc.b	8
		1120.2.cc.c	80
1120.2.cg	\(\chi_{1120}(141, \cdot)\)	n/a	384	4
1120.2.ch	\(\chi_{1120}(139, \cdot)\)	n/a	752	4
1120.2.ci	\(\chi_{1120}(13, \cdot)\)	n/a	752	4
1120.2.cj	\(\chi_{1120}(43, \cdot)\)	n/a	576	4
1120.2.cm	\(\chi_{1120}(267, \cdot)\)	n/a	576	4
1120.2.cn	\(\chi_{1120}(237, \cdot)\)	n/a	752	4
1120.2.cs	\(\chi_{1120}(251, \cdot)\)	n/a	512	4
1120.2.ct	\(\chi_{1120}(29, \cdot)\)	n/a	576	4
1120.2.cv	\(\chi_{1120}(23, \cdot)\)	None	0	4
1120.2.cx	\(\chi_{1120}(73, \cdot)\)	None	0	4
1120.2.cy	\(\chi_{1120}(33, \cdot)\)	n/a	192	4
1120.2.db	\(\chi_{1120}(207, \cdot)\)	n/a	176	4
1120.2.de	\(\chi_{1120}(199, \cdot)\)	None	0	4
1120.2.df	\(\chi_{1120}(121, \cdot)\)	None	0	4
1120.2.dg	\(\chi_{1120}(311, \cdot)\)	None	0	4
1120.2.dh	\(\chi_{1120}(9, \cdot)\)	None	0	4
1120.2.dk	\(\chi_{1120}(543, \cdot)\)	n/a	192	4
1120.2.dn	\(\chi_{1120}(17, \cdot)\)	n/a	176	4
1120.2.dp	\(\chi_{1120}(297, \cdot)\)	None	0	4
1120.2.dr	\(\chi_{1120}(247, \cdot)\)	None	0	4
1120.2.ds	\(\chi_{1120}(109, \cdot)\)	n/a	1504	8
1120.2.dt	\(\chi_{1120}(131, \cdot)\)	n/a	1024	8
1120.2.dy	\(\chi_{1120}(107, \cdot)\)	n/a	1504	8
1120.2.dz	\(\chi_{1120}(157, \cdot)\)	n/a	1504	8
1120.2.ec	\(\chi_{1120}(117, \cdot)\)	n/a	1504	8
1120.2.ed	\(\chi_{1120}(67, \cdot)\)	n/a	1504	8
1120.2.ee	\(\chi_{1120}(19, \cdot)\)	n/a	1504	8
1120.2.ef	\(\chi_{1120}(221, \cdot)\)	n/a	1024	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1120))\) into lower level spaces

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