Space of modular forms of level 560 and weight 4

• Label: 560.4
• Level: 560
• Weight: 4
• Dimension: 13526
• Nonzero newspaces: 28
• Sturm bound: 73728
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(73728\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(560))\).

	Total	New	Old
Modular forms	28320	13798	14522
Cusp forms	26976	13526	13450
Eisenstein series	1344	272	1072

Trace form

13526 * q - 16 * q^2 + 2 * q^3 + 24 * q^4 - 33 * q^5 - 168 * q^6 - 60 * q^7 - 208 * q^8 - 42 * q^9 - 156 * q^10 + 218 * q^11 + 392 * q^12 + 260 * q^13 + 360 * q^14 - 282 * q^15 + 1080 * q^16 - 42 * q^17 + 688 * q^18 - 206 * q^19 - 412 * q^20 - 70 * q^21 - 2384 * q^22 - 202 * q^23 - 3400 * q^24 - 825 * q^25 - 1096 * q^26 - 400 * q^27 + 32 * q^28 - 1220 * q^29 - 812 * q^30 + 834 * q^31 + 2504 * q^32 + 730 * q^33 + 2888 * q^34 + 1253 * q^35 + 960 * q^36 + 3454 * q^37 - 792 * q^38 + 2672 * q^39 + 3548 * q^40 + 1572 * q^41 - 3920 * q^42 - 3932 * q^43 - 1800 * q^44 - 932 * q^45 - 96 * q^46 - 4586 * q^47 + 2600 * q^48 + 7226 * q^49 - 3184 * q^50 - 3994 * q^51 + 848 * q^52 - 890 * q^53 + 8840 * q^54 - 1258 * q^55 + 8208 * q^56 + 6180 * q^57 + 8256 * q^58 + 7302 * q^59 + 6500 * q^60 + 6366 * q^61 + 2480 * q^62 + 536 * q^63 + 6888 * q^64 - 5326 * q^65 - 1768 * q^66 - 2878 * q^67 - 9712 * q^68 - 2892 * q^69 - 6516 * q^70 + 4664 * q^71 - 13448 * q^72 + 5550 * q^73 - 10440 * q^74 + 12879 * q^75 - 13528 * q^76 - 4166 * q^77 - 26656 * q^78 - 4526 * q^79 - 17956 * q^80 - 1256 * q^81 - 14632 * q^82 - 2616 * q^83 - 5064 * q^84 + 2610 * q^85 + 10280 * q^86 + 4400 * q^87 + 4872 * q^88 - 1790 * q^89 + 13804 * q^90 - 12528 * q^91 + 19016 * q^92 - 19574 * q^93 + 29752 * q^94 - 21495 * q^95 + 37896 * q^96 - 4956 * q^97 + 17480 * q^98 - 8952 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(560))\)

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
560.4.a	\(\chi_{560}(1, \cdot)\)	560.4.a.a	1	1
		560.4.a.b	1
		560.4.a.c	1
		560.4.a.d	1
		560.4.a.e	1
		560.4.a.f	1
		560.4.a.g	1
		560.4.a.h	1
		560.4.a.i	1
		560.4.a.j	1
		560.4.a.k	1
		560.4.a.l	1
		560.4.a.m	1
		560.4.a.n	1
		560.4.a.o	1
		560.4.a.p	1
		560.4.a.q	1
		560.4.a.r	2
		560.4.a.s	2
		560.4.a.t	3
		560.4.a.u	3
		560.4.a.v	3
		560.4.a.w	3
		560.4.a.x	3
560.4.b	\(\chi_{560}(281, \cdot)\)	None	0	1
560.4.e	\(\chi_{560}(559, \cdot)\)	560.4.e.a	4	1
		560.4.e.b	4
		560.4.e.c	8
		560.4.e.d	16
		560.4.e.e	40
560.4.g	\(\chi_{560}(449, \cdot)\)	560.4.g.a	2	1
		560.4.g.b	2
		560.4.g.c	2
		560.4.g.d	4
		560.4.g.e	6
		560.4.g.f	10
		560.4.g.g	12
		560.4.g.h	16
560.4.h	\(\chi_{560}(391, \cdot)\)	None	0	1
560.4.k	\(\chi_{560}(111, \cdot)\)	560.4.k.a	16	1
		560.4.k.b	32
560.4.l	\(\chi_{560}(169, \cdot)\)	None	0	1
560.4.n	\(\chi_{560}(279, \cdot)\)	None	0	1
560.4.q	\(\chi_{560}(81, \cdot)\)	560.4.q.a	2	2
		560.4.q.b	2
		560.4.q.c	2
		560.4.q.d	2
		560.4.q.e	2
		560.4.q.f	2
		560.4.q.g	2
		560.4.q.h	4
		560.4.q.i	4
		560.4.q.j	4
		560.4.q.k	4
		560.4.q.l	4
		560.4.q.m	6
		560.4.q.n	10
		560.4.q.o	10
		560.4.q.p	12
		560.4.q.q	12
		560.4.q.r	12
560.4.r	\(\chi_{560}(237, \cdot)\)	n/a	568	2
560.4.t	\(\chi_{560}(43, \cdot)\)	n/a	432	2
560.4.w	\(\chi_{560}(153, \cdot)\)	None	0	2
560.4.x	\(\chi_{560}(127, \cdot)\)	n/a	108	2
560.4.bb	\(\chi_{560}(29, \cdot)\)	n/a	432	2
560.4.bc	\(\chi_{560}(251, \cdot)\)	n/a	384	2
560.4.bd	\(\chi_{560}(141, \cdot)\)	n/a	288	2
560.4.be	\(\chi_{560}(139, \cdot)\)	n/a	568	2
560.4.bi	\(\chi_{560}(183, \cdot)\)	None	0	2
560.4.bj	\(\chi_{560}(97, \cdot)\)	n/a	140	2
560.4.bl	\(\chi_{560}(267, \cdot)\)	n/a	432	2
560.4.bn	\(\chi_{560}(13, \cdot)\)	n/a	568	2
560.4.bq	\(\chi_{560}(199, \cdot)\)	None	0	2
560.4.bs	\(\chi_{560}(31, \cdot)\)	560.4.bs.a	32	2
		560.4.bs.b	32
		560.4.bs.c	32
560.4.bv	\(\chi_{560}(9, \cdot)\)	None	0	2
560.4.bw	\(\chi_{560}(289, \cdot)\)	n/a	140	2
560.4.bz	\(\chi_{560}(311, \cdot)\)	None	0	2
560.4.cb	\(\chi_{560}(121, \cdot)\)	None	0	2
560.4.cc	\(\chi_{560}(159, \cdot)\)	n/a	144	2
560.4.cf	\(\chi_{560}(107, \cdot)\)	n/a	1136	4
560.4.ch	\(\chi_{560}(117, \cdot)\)	n/a	1136	4
560.4.ci	\(\chi_{560}(17, \cdot)\)	n/a	280	4
560.4.cl	\(\chi_{560}(23, \cdot)\)	None	0	4
560.4.co	\(\chi_{560}(19, \cdot)\)	n/a	1136	4
560.4.cp	\(\chi_{560}(221, \cdot)\)	n/a	768	4
560.4.cq	\(\chi_{560}(131, \cdot)\)	n/a	768	4
560.4.cr	\(\chi_{560}(109, \cdot)\)	n/a	1136	4
560.4.cu	\(\chi_{560}(207, \cdot)\)	n/a	288	4
560.4.cx	\(\chi_{560}(73, \cdot)\)	None	0	4
560.4.cz	\(\chi_{560}(157, \cdot)\)	n/a	1136	4
560.4.db	\(\chi_{560}(67, \cdot)\)	n/a	1136	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

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