Space of modular forms of level 1280 and weight 2

• Label: 1280.2
• Level: 1280
• Weight: 2
• Dimension: 25032
• Nonzero newspaces: 22
• Sturm bound: 196608
• Trace bound: 50

Defining parameters

Level:	\( N \)	=	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 22 \)
Sturm bound:			\(196608\)
Trace bound:			\(50\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1280))\).

	Total	New	Old
Modular forms	50560	25656	24904
Cusp forms	47745	25032	22713
Eisenstein series	2815	624	2191

Trace form

25032 * q - 64 * q^2 - 48 * q^3 - 64 * q^4 - 96 * q^5 - 192 * q^6 - 48 * q^7 - 64 * q^8 - 80 * q^9 - 96 * q^10 - 144 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 72 * q^15 - 192 * q^16 - 96 * q^17 - 64 * q^18 - 48 * q^19 - 96 * q^20 - 192 * q^21 - 64 * q^22 - 48 * q^23 - 64 * q^24 - 120 * q^25 - 192 * q^26 - 48 * q^27 - 64 * q^28 - 64 * q^29 - 96 * q^30 - 128 * q^31 - 64 * q^32 - 112 * q^33 - 64 * q^34 - 72 * q^35 - 192 * q^36 - 64 * q^37 - 64 * q^38 - 48 * q^39 - 96 * q^40 - 240 * q^41 - 64 * q^42 - 48 * q^43 - 64 * q^44 - 72 * q^45 - 192 * q^46 - 48 * q^47 - 64 * q^48 - 40 * q^49 - 96 * q^50 - 80 * q^51 - 64 * q^52 - 64 * q^54 - 8 * q^55 - 192 * q^56 + 48 * q^57 - 64 * q^58 + 80 * q^59 - 96 * q^60 - 64 * q^61 - 64 * q^62 + 96 * q^63 - 64 * q^64 - 152 * q^65 - 192 * q^66 + 112 * q^67 - 64 * q^68 + 64 * q^69 - 96 * q^70 - 16 * q^71 - 64 * q^72 + 48 * q^73 - 64 * q^74 - 8 * q^75 - 192 * q^76 - 64 * q^78 + 16 * q^79 - 96 * q^80 - 216 * q^81 - 64 * q^82 - 48 * q^83 - 64 * q^84 - 56 * q^85 - 192 * q^86 - 48 * q^87 - 64 * q^88 - 80 * q^89 - 96 * q^90 - 144 * q^91 - 64 * q^92 - 160 * q^93 - 64 * q^94 - 64 * q^95 - 192 * q^96 - 112 * q^97 - 64 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1280))\)

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
1280.2.a	\(\chi_{1280}(1, \cdot)\)	1280.2.a.a	2	1
		1280.2.a.b	2
		1280.2.a.c	2
		1280.2.a.d	2
		1280.2.a.e	2
		1280.2.a.f	2
		1280.2.a.g	2
		1280.2.a.h	2
		1280.2.a.i	2
		1280.2.a.j	2
		1280.2.a.k	2
		1280.2.a.l	2
		1280.2.a.m	2
		1280.2.a.n	2
		1280.2.a.o	2
		1280.2.a.p	2
1280.2.c	\(\chi_{1280}(769, \cdot)\)	1280.2.c.a	2	1
		1280.2.c.b	2
		1280.2.c.c	2
		1280.2.c.d	2
		1280.2.c.e	4
		1280.2.c.f	4
		1280.2.c.g	4
		1280.2.c.h	4
		1280.2.c.i	4
		1280.2.c.j	4
		1280.2.c.k	4
		1280.2.c.l	4
		1280.2.c.m	4
1280.2.d	\(\chi_{1280}(641, \cdot)\)	1280.2.d.a	2	1
		1280.2.d.b	2
		1280.2.d.c	2
		1280.2.d.d	2
		1280.2.d.e	2
		1280.2.d.f	2
		1280.2.d.g	2
		1280.2.d.h	2
		1280.2.d.i	2
		1280.2.d.j	2
		1280.2.d.k	4
		1280.2.d.l	4
		1280.2.d.m	4
1280.2.f	\(\chi_{1280}(129, \cdot)\)	1280.2.f.a	2	1
		1280.2.f.b	2
		1280.2.f.c	2
		1280.2.f.d	2
		1280.2.f.e	2
		1280.2.f.f	2
		1280.2.f.g	4
		1280.2.f.h	4
		1280.2.f.i	6
		1280.2.f.j	6
		1280.2.f.k	6
		1280.2.f.l	6
1280.2.j	\(\chi_{1280}(63, \cdot)\)	1280.2.j.a	16	2
		1280.2.j.b	16
		1280.2.j.c	32
		1280.2.j.d	32
1280.2.l	\(\chi_{1280}(321, \cdot)\)	1280.2.l.a	8	2
		1280.2.l.b	8
		1280.2.l.c	8
		1280.2.l.d	8
		1280.2.l.e	8
		1280.2.l.f	8
		1280.2.l.g	8
		1280.2.l.h	8
1280.2.n	\(\chi_{1280}(767, \cdot)\)	1280.2.n.a	2	2
		1280.2.n.b	2
		1280.2.n.c	2
		1280.2.n.d	2
		1280.2.n.e	2
		1280.2.n.f	2
		1280.2.n.g	2
		1280.2.n.h	2
		1280.2.n.i	2
		1280.2.n.j	2
		1280.2.n.k	2
		1280.2.n.l	2
		1280.2.n.m	8
		1280.2.n.n	8
		1280.2.n.o	8
		1280.2.n.p	8
		1280.2.n.q	8
		1280.2.n.r	12
		1280.2.n.s	12
1280.2.o	\(\chi_{1280}(127, \cdot)\)	1280.2.o.a	2	2
		1280.2.o.b	2
		1280.2.o.c	2
		1280.2.o.d	2
		1280.2.o.e	2
		1280.2.o.f	2
		1280.2.o.g	2
		1280.2.o.h	2
		1280.2.o.i	2
		1280.2.o.j	2
		1280.2.o.k	2
		1280.2.o.l	2
		1280.2.o.m	2
		1280.2.o.n	2
		1280.2.o.o	2
		1280.2.o.p	2
		1280.2.o.q	4
		1280.2.o.r	4
		1280.2.o.s	12
		1280.2.o.t	12
		1280.2.o.u	12
		1280.2.o.v	12
1280.2.q	\(\chi_{1280}(449, \cdot)\)	1280.2.q.a	16	2
		1280.2.q.b	16
		1280.2.q.c	32
		1280.2.q.d	32
1280.2.s	\(\chi_{1280}(703, \cdot)\)	1280.2.s.a	16	2
		1280.2.s.b	16
		1280.2.s.c	32
		1280.2.s.d	32
1280.2.u	\(\chi_{1280}(543, \cdot)\)	n/a	176	4
1280.2.x	\(\chi_{1280}(161, \cdot)\)	n/a	128	4
1280.2.z	\(\chi_{1280}(289, \cdot)\)	n/a	176	4
1280.2.ba	\(\chi_{1280}(223, \cdot)\)	n/a	176	4
1280.2.bd	\(\chi_{1280}(47, \cdot)\)	n/a	368	8
1280.2.be	\(\chi_{1280}(81, \cdot)\)	n/a	256	8
1280.2.bf	\(\chi_{1280}(49, \cdot)\)	n/a	368	8
1280.2.bj	\(\chi_{1280}(207, \cdot)\)	n/a	368	8
1280.2.bl	\(\chi_{1280}(7, \cdot)\)	None	0	16
1280.2.bm	\(\chi_{1280}(41, \cdot)\)	None	0	16
1280.2.bo	\(\chi_{1280}(9, \cdot)\)	None	0	16
1280.2.br	\(\chi_{1280}(87, \cdot)\)	None	0	16
1280.2.bt	\(\chi_{1280}(3, \cdot)\)	n/a	6080	32
1280.2.bv	\(\chi_{1280}(21, \cdot)\)	n/a	4096	32
1280.2.bw	\(\chi_{1280}(29, \cdot)\)	n/a	6080	32
1280.2.by	\(\chi_{1280}(43, \cdot)\)	n/a	6080	32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 2}\)