Space of modular forms of level 640 and weight 2

• Label: 640.2
• Level: 640
• Weight: 2
• Dimension: 6192
• Nonzero newspaces: 18
• Newform subspaces: 66
• Sturm bound: 49152
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 66 \)
Sturm bound:			\(49152\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(640))\).

	Total	New	Old
Modular forms	12928	6480	6448
Cusp forms	11649	6192	5457
Eisenstein series	1279	288	991

Trace form

6192 * 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 - 72 * q^21 - 32 * q^22 - 8 * q^23 - 32 * q^24 - 44 * q^25 - 96 * q^26 + 24 * q^27 - 32 * q^28 - 48 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^34 - 12 * q^35 - 96 * q^36 - 32 * q^38 + 24 * q^39 - 48 * q^40 - 88 * q^41 - 32 * q^42 - 8 * q^43 - 32 * q^44 - 52 * q^45 - 96 * q^46 - 16 * q^47 - 32 * q^48 - 104 * q^49 - 96 * q^50 - 80 * q^51 - 224 * q^52 - 96 * q^53 - 288 * q^54 - 68 * q^55 - 320 * q^56 - 168 * q^57 - 320 * q^58 - 88 * q^59 - 240 * q^60 - 224 * q^61 - 224 * q^62 - 144 * q^63 - 416 * q^64 - 112 * q^65 - 480 * q^66 - 104 * q^67 - 224 * q^68 - 136 * q^69 - 240 * q^70 - 136 * q^71 - 320 * q^72 - 168 * q^73 - 256 * q^74 - 68 * q^75 - 352 * q^76 - 40 * q^77 - 224 * q^78 - 32 * q^79 - 96 * q^80 - 152 * q^81 - 32 * q^82 + 56 * q^83 - 32 * q^84 - 56 * q^85 - 96 * q^86 + 88 * q^87 - 32 * q^88 + 88 * q^89 - 48 * q^90 + 24 * q^91 - 32 * q^92 + 64 * q^93 - 32 * q^94 + 24 * q^95 - 96 * q^96 + 64 * q^97 - 32 * q^98 + 80 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(640))\)

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
640.2.a	\(\chi_{640}(1, \cdot)\)	640.2.a.a	1	1
		640.2.a.b	1
		640.2.a.c	1
		640.2.a.d	1
		640.2.a.e	1
		640.2.a.f	1
		640.2.a.g	1
		640.2.a.h	1
		640.2.a.i	2
		640.2.a.j	2
		640.2.a.k	2
		640.2.a.l	2
640.2.c	\(\chi_{640}(129, \cdot)\)	640.2.c.a	6	1
		640.2.c.b	6
		640.2.c.c	6
		640.2.c.d	6
640.2.d	\(\chi_{640}(321, \cdot)\)	640.2.d.a	4	1
		640.2.d.b	4
		640.2.d.c	4
		640.2.d.d	4
640.2.f	\(\chi_{640}(449, \cdot)\)	640.2.f.a	2	1
		640.2.f.b	2
		640.2.f.c	4
		640.2.f.d	4
		640.2.f.e	4
		640.2.f.f	4
		640.2.f.g	4
640.2.j	\(\chi_{640}(543, \cdot)\)	640.2.j.a	2	2
		640.2.j.b	2
		640.2.j.c	18
		640.2.j.d	18
640.2.l	\(\chi_{640}(161, \cdot)\)	640.2.l.a	16	2
		640.2.l.b	16
640.2.n	\(\chi_{640}(127, \cdot)\)	640.2.n.a	12	2
		640.2.n.b	12
		640.2.n.c	12
		640.2.n.d	12
640.2.o	\(\chi_{640}(63, \cdot)\)	640.2.o.a	2	2
		640.2.o.b	2
		640.2.o.c	2
		640.2.o.d	2
		640.2.o.e	2
		640.2.o.f	2
		640.2.o.g	2
		640.2.o.h	2
		640.2.o.i	8
		640.2.o.j	12
		640.2.o.k	12
640.2.q	\(\chi_{640}(289, \cdot)\)	640.2.q.a	2	2
		640.2.q.b	2
		640.2.q.c	2
		640.2.q.d	2
		640.2.q.e	16
		640.2.q.f	16
640.2.s	\(\chi_{640}(223, \cdot)\)	640.2.s.a	2	2
		640.2.s.b	2
		640.2.s.c	18
		640.2.s.d	18
640.2.u	\(\chi_{640}(47, \cdot)\)	640.2.u.a	88	4
640.2.x	\(\chi_{640}(81, \cdot)\)	640.2.x.a	64	4
640.2.z	\(\chi_{640}(49, \cdot)\)	640.2.z.a	88	4
640.2.ba	\(\chi_{640}(207, \cdot)\)	640.2.ba.a	88	4
640.2.bd	\(\chi_{640}(87, \cdot)\)	None	0	8
640.2.be	\(\chi_{640}(41, \cdot)\)	None	0	8
640.2.bf	\(\chi_{640}(9, \cdot)\)	None	0	8
640.2.bj	\(\chi_{640}(7, \cdot)\)	None	0	8
640.2.bl	\(\chi_{640}(3, \cdot)\)	640.2.bl.a	1504	16
640.2.bm	\(\chi_{640}(21, \cdot)\)	640.2.bm.a	1024	16
640.2.bo	\(\chi_{640}(29, \cdot)\)	640.2.bo.a	1504	16
640.2.br	\(\chi_{640}(43, \cdot)\)	640.2.br.a	1504	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(640))\) into lower level spaces

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