Space of modular forms of level 560 and weight 5

• Label: 560.5
• Level: 560
• Weight: 5
• Dimension: 18082
• Nonzero newspaces: 28
• Sturm bound: 92160
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(92160\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(560))\).

	Total	New	Old
Modular forms	37536	18350	19186
Cusp forms	36192	18082	18110
Eisenstein series	1344	268	1076

Trace form

18082 * q - 16 * q^2 - 14 * q^3 - 40 * q^4 + 43 * q^5 + 216 * q^6 - 20 * q^7 - 400 * q^8 - 894 * q^9 - 220 * q^10 + 346 * q^11 - 1336 * q^12 + 920 * q^13 + 72 * q^14 + 1302 * q^15 - 712 * q^16 - 82 * q^17 + 5552 * q^18 - 5322 * q^19 + 3780 * q^20 + 786 * q^21 + 3568 * q^22 + 6026 * q^23 - 7496 * q^24 - 2845 * q^25 - 13704 * q^26 - 4412 * q^27 - 5536 * q^28 - 484 * q^29 + 4596 * q^30 - 8606 * q^31 + 4424 * q^32 - 6046 * q^33 + 2504 * q^34 - 2137 * q^35 + 21568 * q^36 - 8034 * q^37 + 5864 * q^38 + 20740 * q^39 + 2332 * q^40 + 11264 * q^41 + 14960 * q^42 + 24064 * q^43 + 11576 * q^44 + 23266 * q^45 + 5344 * q^46 - 17286 * q^47 - 34136 * q^48 - 86438 * q^49 + 5104 * q^50 - 26190 * q^51 - 33840 * q^52 - 16770 * q^53 - 13560 * q^54 - 8012 * q^55 + 4688 * q^56 + 11444 * q^57 - 27904 * q^58 + 8438 * q^59 + 15844 * q^60 + 31830 * q^61 + 67504 * q^62 + 37756 * q^63 + 64424 * q^64 - 7448 * q^65 + 88024 * q^66 - 8238 * q^67 + 39120 * q^68 - 31960 * q^69 - 7700 * q^70 - 42532 * q^71 - 9544 * q^72 - 3730 * q^73 + 13112 * q^74 - 39599 * q^75 - 41112 * q^76 + 32710 * q^77 + 15136 * q^78 + 47694 * q^79 - 22692 * q^80 - 6404 * q^81 - 10600 * q^82 + 16312 * q^83 - 69448 * q^84 + 18850 * q^85 - 129432 * q^86 - 1880 * q^87 - 121336 * q^88 + 2730 * q^89 - 182164 * q^90 + 18412 * q^91 - 163256 * q^92 + 26970 * q^93 - 183368 * q^94 - 25595 * q^95 + 116488 * q^96 - 5880 * q^97 + 119304 * q^98 - 35724 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(560))\)

We only show spaces with odd 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
560.5.c	\(\chi_{560}(489, \cdot)\)	None	0	1
560.5.d	\(\chi_{560}(351, \cdot)\)	560.5.d.a	16	1
		560.5.d.b	32
560.5.f	\(\chi_{560}(321, \cdot)\)	560.5.f.a	8	1
		560.5.f.b	12
		560.5.f.c	12
		560.5.f.d	32
560.5.i	\(\chi_{560}(519, \cdot)\)	None	0	1
560.5.j	\(\chi_{560}(239, \cdot)\)	560.5.j.a	24	1
		560.5.j.b	48
560.5.m	\(\chi_{560}(41, \cdot)\)	None	0	1
560.5.o	\(\chi_{560}(71, \cdot)\)	None	0	1
560.5.p	\(\chi_{560}(209, \cdot)\)	560.5.p.a	1	1
		560.5.p.b	1
		560.5.p.c	2
		560.5.p.d	2
		560.5.p.e	2
		560.5.p.f	2
		560.5.p.g	8
		560.5.p.h	12
		560.5.p.i	16
		560.5.p.j	48
560.5.s	\(\chi_{560}(197, \cdot)\)	n/a	576	2
560.5.u	\(\chi_{560}(27, \cdot)\)	n/a	760	2
560.5.v	\(\chi_{560}(223, \cdot)\)	n/a	192	2
560.5.y	\(\chi_{560}(57, \cdot)\)	None	0	2
560.5.z	\(\chi_{560}(181, \cdot)\)	n/a	512	2
560.5.ba	\(\chi_{560}(99, \cdot)\)	n/a	576	2
560.5.bf	\(\chi_{560}(69, \cdot)\)	n/a	760	2
560.5.bg	\(\chi_{560}(211, \cdot)\)	n/a	384	2
560.5.bh	\(\chi_{560}(113, \cdot)\)	n/a	144	2
560.5.bk	\(\chi_{560}(167, \cdot)\)	None	0	2
560.5.bm	\(\chi_{560}(307, \cdot)\)	n/a	760	2
560.5.bo	\(\chi_{560}(477, \cdot)\)	n/a	576	2
560.5.bp	\(\chi_{560}(151, \cdot)\)	None	0	2
560.5.br	\(\chi_{560}(129, \cdot)\)	n/a	188	2
560.5.bt	\(\chi_{560}(79, \cdot)\)	n/a	192	2
560.5.bu	\(\chi_{560}(201, \cdot)\)	None	0	2
560.5.bx	\(\chi_{560}(241, \cdot)\)	n/a	128	2
560.5.by	\(\chi_{560}(39, \cdot)\)	None	0	2
560.5.ca	\(\chi_{560}(89, \cdot)\)	None	0	2
560.5.cd	\(\chi_{560}(191, \cdot)\)	n/a	128	2
560.5.ce	\(\chi_{560}(227, \cdot)\)	n/a	1520	4
560.5.cg	\(\chi_{560}(53, \cdot)\)	n/a	1520	4
560.5.cj	\(\chi_{560}(87, \cdot)\)	None	0	4
560.5.ck	\(\chi_{560}(177, \cdot)\)	n/a	376	4
560.5.cm	\(\chi_{560}(11, \cdot)\)	n/a	1024	4
560.5.cn	\(\chi_{560}(229, \cdot)\)	n/a	1520	4
560.5.cs	\(\chi_{560}(179, \cdot)\)	n/a	1520	4
560.5.ct	\(\chi_{560}(61, \cdot)\)	n/a	1024	4
560.5.cv	\(\chi_{560}(137, \cdot)\)	None	0	4
560.5.cw	\(\chi_{560}(47, \cdot)\)	n/a	384	4
560.5.cy	\(\chi_{560}(37, \cdot)\)	n/a	1520	4
560.5.da	\(\chi_{560}(3, \cdot)\)	n/a	1520	4

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

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