Space of modular forms of level 560 and weight 3

• Label: 560.3
• Level: 560
• Weight: 3
• Dimension: 8974
• Nonzero newspaces: 28
• Sturm bound: 55296
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(55296\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(560))\).

	Total	New	Old
Modular forms	19104	9242	9862
Cusp forms	17760	8974	8786
Eisenstein series	1344	268	1076

Trace form

8974 * q - 16 * q^2 - 14 * q^3 - 40 * q^4 - 41 * q^5 - 72 * q^6 - 20 * q^7 - 16 * q^8 + 30 * q^9 + 52 * q^10 - 102 * q^11 + 200 * q^12 - 32 * q^13 + 8 * q^14 - 138 * q^15 - 200 * q^16 - 186 * q^17 - 304 * q^18 + 22 * q^19 - 188 * q^20 - 222 * q^21 - 240 * q^22 + 186 * q^23 + 184 * q^24 + 15 * q^25 + 344 * q^26 + 484 * q^27 + 224 * q^28 + 340 * q^29 + 660 * q^30 + 290 * q^31 + 584 * q^32 + 674 * q^33 + 328 * q^34 + 71 * q^35 + 64 * q^36 + 294 * q^37 + 264 * q^38 - 572 * q^39 - 100 * q^40 - 72 * q^41 + 560 * q^42 - 464 * q^43 + 568 * q^44 - 74 * q^45 + 256 * q^46 - 198 * q^47 + 424 * q^48 - 426 * q^49 - 624 * q^50 + 258 * q^51 + 208 * q^52 + 342 * q^53 - 120 * q^54 + 212 * q^55 - 560 * q^56 - 556 * q^57 - 1216 * q^58 + 630 * q^59 - 1436 * q^60 - 530 * q^61 - 2096 * q^62 + 124 * q^63 - 2008 * q^64 - 200 * q^65 - 3560 * q^66 + 290 * q^67 - 2352 * q^68 - 1528 * q^69 - 1412 * q^70 - 324 * q^71 - 3016 * q^72 - 522 * q^73 - 1256 * q^74 + 481 * q^75 - 1176 * q^76 - 874 * q^77 - 608 * q^78 - 354 * q^79 + 604 * q^80 - 56 * q^81 + 1624 * q^82 + 88 * q^83 + 1208 * q^84 - 886 * q^85 + 1928 * q^86 - 632 * q^87 + 1544 * q^88 + 18 * q^89 + 1868 * q^90 + 1132 * q^91 + 968 * q^92 + 234 * q^93 - 584 * q^94 + 61 * q^95 - 1784 * q^96 + 880 * q^97 - 1528 * q^98 + 2532 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(560))\)

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
560.3.c	\(\chi_{560}(489, \cdot)\)	None	0	1
560.3.d	\(\chi_{560}(351, \cdot)\)	560.3.d.a	8	1
		560.3.d.b	16
560.3.f	\(\chi_{560}(321, \cdot)\)	560.3.f.a	2	1
		560.3.f.b	2
		560.3.f.c	4
		560.3.f.d	8
		560.3.f.e	16
560.3.i	\(\chi_{560}(519, \cdot)\)	None	0	1
560.3.j	\(\chi_{560}(239, \cdot)\)	560.3.j.a	12	1
		560.3.j.b	24
560.3.m	\(\chi_{560}(41, \cdot)\)	None	0	1
560.3.o	\(\chi_{560}(71, \cdot)\)	None	0	1
560.3.p	\(\chi_{560}(209, \cdot)\)	560.3.p.a	1	1
		560.3.p.b	1
		560.3.p.c	2
		560.3.p.d	2
		560.3.p.e	4
		560.3.p.f	4
		560.3.p.g	8
		560.3.p.h	24
560.3.s	\(\chi_{560}(197, \cdot)\)	n/a	288	2
560.3.u	\(\chi_{560}(27, \cdot)\)	n/a	376	2
560.3.v	\(\chi_{560}(223, \cdot)\)	560.3.v.a	32	2
		560.3.v.b	64
560.3.y	\(\chi_{560}(57, \cdot)\)	None	0	2
560.3.z	\(\chi_{560}(181, \cdot)\)	n/a	256	2
560.3.ba	\(\chi_{560}(99, \cdot)\)	n/a	288	2
560.3.bf	\(\chi_{560}(69, \cdot)\)	n/a	376	2
560.3.bg	\(\chi_{560}(211, \cdot)\)	n/a	192	2
560.3.bh	\(\chi_{560}(113, \cdot)\)	560.3.bh.a	4	2
		560.3.bh.b	4
		560.3.bh.c	8
		560.3.bh.d	8
		560.3.bh.e	12
		560.3.bh.f	16
		560.3.bh.g	20
560.3.bk	\(\chi_{560}(167, \cdot)\)	None	0	2
560.3.bm	\(\chi_{560}(307, \cdot)\)	n/a	376	2
560.3.bo	\(\chi_{560}(477, \cdot)\)	n/a	288	2
560.3.bp	\(\chi_{560}(151, \cdot)\)	None	0	2
560.3.br	\(\chi_{560}(129, \cdot)\)	560.3.br.a	12	2
		560.3.br.b	16
		560.3.br.c	16
		560.3.br.d	48
560.3.bt	\(\chi_{560}(79, \cdot)\)	560.3.bt.a	8	2
		560.3.bt.b	24
		560.3.bt.c	32
		560.3.bt.d	32
560.3.bu	\(\chi_{560}(201, \cdot)\)	None	0	2
560.3.bx	\(\chi_{560}(241, \cdot)\)	560.3.bx.a	8	2
		560.3.bx.b	12
		560.3.bx.c	12
		560.3.bx.d	32
560.3.by	\(\chi_{560}(39, \cdot)\)	None	0	2
560.3.ca	\(\chi_{560}(89, \cdot)\)	None	0	2
560.3.cd	\(\chi_{560}(191, \cdot)\)	560.3.cd.a	20	2
		560.3.cd.b	20
		560.3.cd.c	24
560.3.ce	\(\chi_{560}(227, \cdot)\)	n/a	752	4
560.3.cg	\(\chi_{560}(53, \cdot)\)	n/a	752	4
560.3.cj	\(\chi_{560}(87, \cdot)\)	None	0	4
560.3.ck	\(\chi_{560}(177, \cdot)\)	n/a	184	4
560.3.cm	\(\chi_{560}(11, \cdot)\)	n/a	512	4
560.3.cn	\(\chi_{560}(229, \cdot)\)	n/a	752	4
560.3.cs	\(\chi_{560}(179, \cdot)\)	n/a	752	4
560.3.ct	\(\chi_{560}(61, \cdot)\)	n/a	512	4
560.3.cv	\(\chi_{560}(137, \cdot)\)	None	0	4
560.3.cw	\(\chi_{560}(47, \cdot)\)	n/a	192	4
560.3.cy	\(\chi_{560}(37, \cdot)\)	n/a	752	4
560.3.da	\(\chi_{560}(3, \cdot)\)	n/a	752	4

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(560))\) into lower level spaces

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