Space of modular forms of level 640 and weight 4

• Label: 640.4
• Level: 640
• Weight: 4
• Dimension: 18864
• Nonzero newspaces: 18
• Sturm bound: 98304
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(98304\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(640))\).

	Total	New	Old
Modular forms	37504	19152	18352
Cusp forms	36224	18864	17360
Eisenstein series	1280	288	992

Trace form

18864 * q - 32 * q^2 - 24 * q^3 - 32 * q^4 - 48 * q^5 - 96 * q^6 - 24 * q^7 - 32 * q^8 - 40 * q^9 - 48 * q^10 - 72 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 96 * q^16 - 48 * q^17 - 32 * q^18 - 24 * q^19 - 48 * q^20 + 120 * q^21 - 32 * q^22 + 632 * q^23 - 32 * q^24 + 116 * q^25 - 96 * q^26 - 552 * q^27 - 32 * q^28 - 832 * q^29 - 48 * q^30 - 1568 * q^31 - 32 * q^32 - 1920 * q^33 - 32 * q^34 - 492 * q^35 - 96 * q^36 - 64 * q^37 - 32 * q^38 + 1176 * q^39 - 48 * q^40 + 1768 * q^41 - 32 * q^42 + 1592 * q^43 - 32 * q^44 + 236 * q^45 - 96 * q^46 - 16 * q^47 - 32 * q^48 - 2792 * q^49 - 5760 * q^50 - 2832 * q^51 - 13280 * q^52 - 3040 * q^53 - 6944 * q^54 - 324 * q^55 + 1472 * q^56 + 2648 * q^57 + 9472 * q^58 + 2728 * q^59 + 9744 * q^60 + 7200 * q^61 + 11680 * q^62 + 4976 * q^63 + 24160 * q^64 + 3856 * q^65 + 21792 * q^66 + 4056 * q^67 + 8224 * q^68 + 4408 * q^69 + 3984 * q^70 + 376 * q^71 - 2624 * q^72 - 3496 * q^73 - 10560 * q^74 - 2244 * q^75 - 23904 * q^76 - 4904 * q^77 - 28256 * q^78 - 32 * q^79 - 10080 * q^80 + 1384 * q^81 - 32 * q^82 + 4856 * q^83 - 32 * q^84 - 568 * q^85 - 96 * q^86 - 2600 * q^87 - 32 * q^88 - 6824 * q^89 - 48 * q^90 - 7272 * q^91 - 32 * q^92 - 8576 * q^93 - 32 * q^94 - 6120 * q^95 - 96 * q^96 - 11968 * q^97 - 32 * q^98 - 10864 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(640))\)

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
640.4.a	\(\chi_{640}(1, \cdot)\)	640.4.a.a	1	1
		640.4.a.b	1
		640.4.a.c	1
		640.4.a.d	1
		640.4.a.e	2
		640.4.a.f	2
		640.4.a.g	2
		640.4.a.h	2
		640.4.a.i	2
		640.4.a.j	2
		640.4.a.k	2
		640.4.a.l	2
		640.4.a.m	3
		640.4.a.n	3
		640.4.a.o	3
		640.4.a.p	3
		640.4.a.q	4
		640.4.a.r	4
		640.4.a.s	4
		640.4.a.t	4
640.4.c	\(\chi_{640}(129, \cdot)\)	640.4.c.a	18	1
		640.4.c.b	18
		640.4.c.c	18
		640.4.c.d	18
640.4.d	\(\chi_{640}(321, \cdot)\)	640.4.d.a	4	1
		640.4.d.b	4
		640.4.d.c	4
		640.4.d.d	4
		640.4.d.e	4
		640.4.d.f	4
		640.4.d.g	8
		640.4.d.h	8
		640.4.d.i	8
640.4.f	\(\chi_{640}(449, \cdot)\)	640.4.f.a	2	1
		640.4.f.b	2
		640.4.f.c	4
		640.4.f.d	4
		640.4.f.e	4
		640.4.f.f	4
		640.4.f.g	4
		640.4.f.h	8
		640.4.f.i	12
		640.4.f.j	12
		640.4.f.k	16
640.4.j	\(\chi_{640}(543, \cdot)\)	n/a	136	2
640.4.l	\(\chi_{640}(161, \cdot)\)	640.4.l.a	48	2
		640.4.l.b	48
640.4.n	\(\chi_{640}(127, \cdot)\)	n/a	144	2
640.4.o	\(\chi_{640}(63, \cdot)\)	n/a	144	2
640.4.q	\(\chi_{640}(289, \cdot)\)	n/a	136	2
640.4.s	\(\chi_{640}(223, \cdot)\)	n/a	136	2
640.4.u	\(\chi_{640}(47, \cdot)\)	n/a	280	4
640.4.x	\(\chi_{640}(81, \cdot)\)	n/a	192	4
640.4.z	\(\chi_{640}(49, \cdot)\)	n/a	280	4
640.4.ba	\(\chi_{640}(207, \cdot)\)	n/a	280	4
640.4.bd	\(\chi_{640}(87, \cdot)\)	None	0	8
640.4.be	\(\chi_{640}(41, \cdot)\)	None	0	8
640.4.bf	\(\chi_{640}(9, \cdot)\)	None	0	8
640.4.bj	\(\chi_{640}(7, \cdot)\)	None	0	8
640.4.bl	\(\chi_{640}(3, \cdot)\)	n/a	4576	16
640.4.bm	\(\chi_{640}(21, \cdot)\)	n/a	3072	16
640.4.bo	\(\chi_{640}(29, \cdot)\)	n/a	4576	16
640.4.br	\(\chi_{640}(43, \cdot)\)	n/a	4576	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(640))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(640)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 1}\)