Space of modular forms of level 560 and weight 2

• Label: 560.2
• Level: 560
• Weight: 2
• Dimension: 4418
• Nonzero newspaces: 28
• Newform subspaces: 89
• Sturm bound: 36864
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Newform subspaces:			\( 89 \)
Sturm bound:			\(36864\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(560))\).

	Total	New	Old
Modular forms	9888	4690	5198
Cusp forms	8545	4418	4127
Eisenstein series	1343	272	1071

Trace form

4418 * q - 16 * q^2 - 14 * q^3 - 8 * q^4 - 29 * q^5 - 24 * q^6 - 12 * q^7 - 16 * q^8 + 2 * q^9 - 20 * q^10 - 22 * q^11 - 24 * q^12 - 4 * q^13 - 24 * q^14 - 10 * q^15 - 72 * q^16 - 18 * q^17 + 50 * q^19 - 12 * q^20 - 22 * q^21 - 32 * q^22 + 54 * q^23 - 8 * q^24 + 35 * q^25 - 24 * q^26 + 16 * q^27 - 32 * q^28 + 4 * q^29 - 92 * q^30 - 62 * q^31 - 56 * q^32 - 38 * q^33 - 120 * q^34 - 19 * q^35 - 256 * q^36 - 42 * q^37 - 168 * q^38 - 64 * q^39 - 196 * q^40 - 68 * q^41 - 240 * q^42 - 28 * q^43 - 232 * q^44 - 120 * q^45 - 240 * q^46 + 22 * q^47 - 344 * q^48 - 106 * q^49 - 192 * q^50 - 42 * q^51 - 304 * q^52 - 114 * q^53 - 440 * q^54 - 26 * q^55 - 240 * q^56 - 124 * q^57 - 224 * q^58 - 10 * q^59 - 124 * q^60 - 186 * q^61 - 160 * q^62 - 104 * q^63 - 152 * q^64 - 14 * q^65 - 136 * q^66 - 142 * q^67 - 16 * q^68 - 108 * q^69 + 4 * q^70 - 136 * q^71 + 56 * q^72 + 86 * q^73 + 168 * q^74 - 185 * q^75 + 136 * q^76 + 74 * q^77 + 224 * q^78 - 110 * q^79 + 156 * q^80 + 68 * q^81 + 120 * q^82 - 88 * q^83 + 120 * q^84 - 22 * q^85 + 88 * q^86 - 160 * q^87 + 200 * q^88 + 138 * q^89 + 284 * q^90 - 192 * q^91 - 24 * q^92 + 154 * q^93 + 184 * q^94 - 167 * q^95 + 264 * q^96 + 76 * q^97 + 136 * q^98 - 408 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)

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
560.2.a	\(\chi_{560}(1, \cdot)\)	560.2.a.a	1	1
		560.2.a.b	1
		560.2.a.c	1
		560.2.a.d	1
		560.2.a.e	1
		560.2.a.f	1
		560.2.a.g	2
		560.2.a.h	2
		560.2.a.i	2
560.2.b	\(\chi_{560}(281, \cdot)\)	None	0	1
560.2.e	\(\chi_{560}(559, \cdot)\)	560.2.e.a	4	1
		560.2.e.b	4
		560.2.e.c	8
		560.2.e.d	8
560.2.g	\(\chi_{560}(449, \cdot)\)	560.2.g.a	2	1
		560.2.g.b	2
		560.2.g.c	2
		560.2.g.d	2
		560.2.g.e	4
		560.2.g.f	6
560.2.h	\(\chi_{560}(391, \cdot)\)	None	0	1
560.2.k	\(\chi_{560}(111, \cdot)\)	560.2.k.a	8	1
		560.2.k.b	8
560.2.l	\(\chi_{560}(169, \cdot)\)	None	0	1
560.2.n	\(\chi_{560}(279, \cdot)\)	None	0	1
560.2.q	\(\chi_{560}(81, \cdot)\)	560.2.q.a	2	2
		560.2.q.b	2
		560.2.q.c	2
		560.2.q.d	2
		560.2.q.e	2
		560.2.q.f	2
		560.2.q.g	2
		560.2.q.h	2
		560.2.q.i	2
		560.2.q.j	4
		560.2.q.k	4
		560.2.q.l	6
560.2.r	\(\chi_{560}(237, \cdot)\)	560.2.r.a	184	2
560.2.t	\(\chi_{560}(43, \cdot)\)	560.2.t.a	144	2
560.2.w	\(\chi_{560}(153, \cdot)\)	None	0	2
560.2.x	\(\chi_{560}(127, \cdot)\)	560.2.x.a	12	2
		560.2.x.b	24
560.2.bb	\(\chi_{560}(29, \cdot)\)	560.2.bb.a	2	2
		560.2.bb.b	2
		560.2.bb.c	70
		560.2.bb.d	70
560.2.bc	\(\chi_{560}(251, \cdot)\)	560.2.bc.a	128	2
560.2.bd	\(\chi_{560}(141, \cdot)\)	560.2.bd.a	44	2
		560.2.bd.b	52
560.2.be	\(\chi_{560}(139, \cdot)\)	560.2.be.a	184	2
560.2.bi	\(\chi_{560}(183, \cdot)\)	None	0	2
560.2.bj	\(\chi_{560}(97, \cdot)\)	560.2.bj.a	4	2
		560.2.bj.b	8
		560.2.bj.c	8
		560.2.bj.d	24
560.2.bl	\(\chi_{560}(267, \cdot)\)	560.2.bl.a	144	2
560.2.bn	\(\chi_{560}(13, \cdot)\)	560.2.bn.a	184	2
560.2.bq	\(\chi_{560}(199, \cdot)\)	None	0	2
560.2.bs	\(\chi_{560}(31, \cdot)\)	560.2.bs.a	8	2
		560.2.bs.b	12
		560.2.bs.c	12
560.2.bv	\(\chi_{560}(9, \cdot)\)	None	0	2
560.2.bw	\(\chi_{560}(289, \cdot)\)	560.2.bw.a	4	2
		560.2.bw.b	4
		560.2.bw.c	4
		560.2.bw.d	4
		560.2.bw.e	4
		560.2.bw.f	24
560.2.bz	\(\chi_{560}(311, \cdot)\)	None	0	2
560.2.cb	\(\chi_{560}(121, \cdot)\)	None	0	2
560.2.cc	\(\chi_{560}(159, \cdot)\)	560.2.cc.a	4	2
		560.2.cc.b	4
		560.2.cc.c	4
		560.2.cc.d	4
		560.2.cc.e	8
		560.2.cc.f	8
		560.2.cc.g	8
		560.2.cc.h	8
560.2.cf	\(\chi_{560}(107, \cdot)\)	560.2.cf.a	368	4
560.2.ch	\(\chi_{560}(117, \cdot)\)	560.2.ch.a	4	4
		560.2.ch.b	4
		560.2.ch.c	360
560.2.ci	\(\chi_{560}(17, \cdot)\)	560.2.ci.a	4	4
		560.2.ci.b	4
		560.2.ci.c	16
		560.2.ci.d	16
		560.2.ci.e	48
560.2.cl	\(\chi_{560}(23, \cdot)\)	None	0	4
560.2.co	\(\chi_{560}(19, \cdot)\)	560.2.co.a	368	4
560.2.cp	\(\chi_{560}(221, \cdot)\)	560.2.cp.a	256	4
560.2.cq	\(\chi_{560}(131, \cdot)\)	560.2.cq.a	256	4
560.2.cr	\(\chi_{560}(109, \cdot)\)	560.2.cr.a	368	4
560.2.cu	\(\chi_{560}(207, \cdot)\)	560.2.cu.a	8	4
		560.2.cu.b	24
		560.2.cu.c	32
		560.2.cu.d	32
560.2.cx	\(\chi_{560}(73, \cdot)\)	None	0	4
560.2.cz	\(\chi_{560}(157, \cdot)\)	560.2.cz.a	4	4
		560.2.cz.b	4
		560.2.cz.c	360
560.2.db	\(\chi_{560}(67, \cdot)\)	560.2.db.a	368	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

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