Space of modular forms of level 560 and weight 6

• Label: 560.6
• Level: 560
• Weight: 6
• Dimension: 22634
• Nonzero newspaces: 28
• Sturm bound: 110592
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(110592\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(560))\).

	Total	New	Old
Modular forms	46752	22906	23846
Cusp forms	45408	22634	22774
Eisenstein series	1344	272	1072

Trace form

22634 * q - 16 * q^2 - 46 * q^3 - 104 * q^4 - 69 * q^5 + 408 * q^6 + 212 * q^7 + 944 * q^8 + 234 * q^9 - 892 * q^10 - 5110 * q^11 + 8 * q^12 + 716 * q^13 - 216 * q^14 + 2070 * q^15 - 3528 * q^16 - 834 * q^17 - 12560 * q^18 - 6606 * q^19 + 5924 * q^20 - 7414 * q^21 + 17648 * q^22 - 3466 * q^23 + 33464 * q^24 - 12501 * q^25 + 29432 * q^26 + 32720 * q^27 - 22880 * q^28 - 4172 * q^29 - 71852 * q^30 - 38974 * q^31 + 6344 * q^32 + 3802 * q^33 + 91464 * q^34 - 11203 * q^35 - 24384 * q^36 - 71322 * q^37 + 63912 * q^38 - 43552 * q^39 - 86436 * q^40 - 43764 * q^41 - 176720 * q^42 - 25820 * q^43 - 135816 * q^44 + 184720 * q^45 + 217312 * q^46 + 313750 * q^47 + 330536 * q^48 + 648286 * q^49 - 61936 * q^50 - 80650 * q^51 - 245680 * q^52 - 225218 * q^53 - 215416 * q^54 - 94330 * q^55 - 116592 * q^56 - 126012 * q^57 + 111424 * q^58 + 51414 * q^59 - 246172 * q^60 - 158282 * q^61 - 475792 * q^62 + 82328 * q^63 + 240232 * q^64 + 70706 * q^65 + 507416 * q^66 + 271634 * q^67 + 82832 * q^68 + 177876 * q^69 - 384596 * q^70 + 254456 * q^71 + 374776 * q^72 - 48506 * q^73 + 685560 * q^74 - 293001 * q^75 + 137128 * q^76 - 210518 * q^77 - 748960 * q^78 - 1103022 * q^79 - 123172 * q^80 + 152812 * q^81 + 361176 * q^82 + 691176 * q^83 + 591672 * q^84 + 120762 * q^85 + 1517672 * q^86 + 1591232 * q^87 + 1115400 * q^88 + 17914 * q^89 - 1729364 * q^90 - 866144 * q^91 - 1349560 * q^92 - 1025030 * q^93 - 726728 * q^94 - 871719 * q^95 - 2362872 * q^96 - 368388 * q^97 - 2081080 * q^98 + 1856616 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(560))\)

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
560.6.a	\(\chi_{560}(1, \cdot)\)	560.6.a.a	1	1
		560.6.a.b	1
		560.6.a.c	1
		560.6.a.d	1
		560.6.a.e	1
		560.6.a.f	1
		560.6.a.g	1
		560.6.a.h	1
		560.6.a.i	1
		560.6.a.j	2
		560.6.a.k	2
		560.6.a.l	2
		560.6.a.m	2
		560.6.a.n	2
		560.6.a.o	2
		560.6.a.p	2
		560.6.a.q	3
		560.6.a.r	3
		560.6.a.s	3
		560.6.a.t	3
		560.6.a.u	3
		560.6.a.v	4
		560.6.a.w	4
		560.6.a.x	4
		560.6.a.y	5
		560.6.a.z	5
560.6.b	\(\chi_{560}(281, \cdot)\)	None	0	1
560.6.e	\(\chi_{560}(559, \cdot)\)	n/a	120	1
560.6.g	\(\chi_{560}(449, \cdot)\)	560.6.g.a	2	1
		560.6.g.b	2
		560.6.g.c	2
		560.6.g.d	10
		560.6.g.e	14
		560.6.g.f	16
		560.6.g.g	20
		560.6.g.h	24
560.6.h	\(\chi_{560}(391, \cdot)\)	None	0	1
560.6.k	\(\chi_{560}(111, \cdot)\)	560.6.k.a	24	1
		560.6.k.b	56
560.6.l	\(\chi_{560}(169, \cdot)\)	None	0	1
560.6.n	\(\chi_{560}(279, \cdot)\)	None	0	1
560.6.q	\(\chi_{560}(81, \cdot)\)	n/a	160	2
560.6.r	\(\chi_{560}(237, \cdot)\)	n/a	952	2
560.6.t	\(\chi_{560}(43, \cdot)\)	n/a	720	2
560.6.w	\(\chi_{560}(153, \cdot)\)	None	0	2
560.6.x	\(\chi_{560}(127, \cdot)\)	n/a	180	2
560.6.bb	\(\chi_{560}(29, \cdot)\)	n/a	720	2
560.6.bc	\(\chi_{560}(251, \cdot)\)	n/a	640	2
560.6.bd	\(\chi_{560}(141, \cdot)\)	n/a	480	2
560.6.be	\(\chi_{560}(139, \cdot)\)	n/a	952	2
560.6.bi	\(\chi_{560}(183, \cdot)\)	None	0	2
560.6.bj	\(\chi_{560}(97, \cdot)\)	n/a	236	2
560.6.bl	\(\chi_{560}(267, \cdot)\)	n/a	720	2
560.6.bn	\(\chi_{560}(13, \cdot)\)	n/a	952	2
560.6.bq	\(\chi_{560}(199, \cdot)\)	None	0	2
560.6.bs	\(\chi_{560}(31, \cdot)\)	n/a	160	2
560.6.bv	\(\chi_{560}(9, \cdot)\)	None	0	2
560.6.bw	\(\chi_{560}(289, \cdot)\)	n/a	236	2
560.6.bz	\(\chi_{560}(311, \cdot)\)	None	0	2
560.6.cb	\(\chi_{560}(121, \cdot)\)	None	0	2
560.6.cc	\(\chi_{560}(159, \cdot)\)	n/a	240	2
560.6.cf	\(\chi_{560}(107, \cdot)\)	n/a	1904	4
560.6.ch	\(\chi_{560}(117, \cdot)\)	n/a	1904	4
560.6.ci	\(\chi_{560}(17, \cdot)\)	n/a	472	4
560.6.cl	\(\chi_{560}(23, \cdot)\)	None	0	4
560.6.co	\(\chi_{560}(19, \cdot)\)	n/a	1904	4
560.6.cp	\(\chi_{560}(221, \cdot)\)	n/a	1280	4
560.6.cq	\(\chi_{560}(131, \cdot)\)	n/a	1280	4
560.6.cr	\(\chi_{560}(109, \cdot)\)	n/a	1904	4
560.6.cu	\(\chi_{560}(207, \cdot)\)	n/a	480	4
560.6.cx	\(\chi_{560}(73, \cdot)\)	None	0	4
560.6.cz	\(\chi_{560}(157, \cdot)\)	n/a	1904	4
560.6.db	\(\chi_{560}(67, \cdot)\)	n/a	1904	4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

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