Space of modular forms of level 1280 and weight 3

• Label: 1280.3
• Level: 1280
• Weight: 3
• Dimension: 50376
• Nonzero newspaces: 22
• Sturm bound: 294912
• Trace bound: 50

Defining parameters

Level:	\( N \)	=	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 22 \)
Sturm bound:			\(294912\)
Trace bound:			\(50\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1280))\).

	Total	New	Old
Modular forms	99712	51000	48712
Cusp forms	96896	50376	46520
Eisenstein series	2816	624	2192

Trace form

50376 * 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 - 160 * 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 - 168 * q^45 - 192 * q^46 - 48 * q^47 - 64 * q^48 - 488 * q^49 - 96 * q^50 - 912 * q^51 - 64 * q^52 - 704 * q^53 - 64 * q^54 - 584 * q^55 - 192 * q^56 - 848 * q^57 - 64 * q^58 - 560 * q^59 - 96 * q^60 - 448 * q^61 - 64 * q^62 - 32 * q^63 - 64 * q^64 - 88 * q^65 - 192 * q^66 + 592 * q^67 - 64 * q^68 + 704 * q^69 - 96 * q^70 + 880 * q^71 - 64 * q^72 + 1200 * q^73 - 64 * q^74 + 696 * q^75 - 192 * q^76 + 832 * q^77 - 64 * q^78 + 976 * q^79 - 96 * q^80 + 360 * q^81 - 64 * q^82 - 48 * q^83 - 64 * q^84 + 104 * q^85 - 192 * q^86 - 48 * q^87 - 64 * q^88 - 80 * q^89 - 96 * q^90 - 144 * q^91 - 64 * q^92 + 224 * q^93 - 64 * q^94 - 80 * q^95 - 192 * q^96 - 112 * q^97 - 64 * q^98 + 96 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1280))\)

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
1280.3.b	\(\chi_{1280}(511, \cdot)\)	1280.3.b.a	4	1
		1280.3.b.b	4
		1280.3.b.c	4
		1280.3.b.d	4
		1280.3.b.e	8
		1280.3.b.f	8
		1280.3.b.g	8
		1280.3.b.h	8
		1280.3.b.i	16
1280.3.e	\(\chi_{1280}(639, \cdot)\)	1280.3.e.a	2	1
		1280.3.e.b	2
		1280.3.e.c	2
		1280.3.e.d	2
		1280.3.e.e	4
		1280.3.e.f	6
		1280.3.e.g	6
		1280.3.e.h	6
		1280.3.e.i	6
		1280.3.e.j	8
		1280.3.e.k	24
		1280.3.e.l	24
1280.3.g	\(\chi_{1280}(1151, \cdot)\)	1280.3.g.a	4	1
		1280.3.g.b	4
		1280.3.g.c	4
		1280.3.g.d	4
		1280.3.g.e	8
		1280.3.g.f	8
		1280.3.g.g	16
		1280.3.g.h	16
1280.3.h	\(\chi_{1280}(1279, \cdot)\)	1280.3.h.a	2	1
		1280.3.h.b	2
		1280.3.h.c	2
		1280.3.h.d	2
		1280.3.h.e	4
		1280.3.h.f	4
		1280.3.h.g	4
		1280.3.h.h	8
		1280.3.h.i	8
		1280.3.h.j	8
		1280.3.h.k	8
		1280.3.h.l	8
		1280.3.h.m	16
		1280.3.h.n	16
1280.3.i	\(\chi_{1280}(833, \cdot)\)	n/a	192	2
1280.3.k	\(\chi_{1280}(319, \cdot)\)	n/a	192	2
1280.3.m	\(\chi_{1280}(897, \cdot)\)	n/a	184	2
1280.3.p	\(\chi_{1280}(257, \cdot)\)	n/a	184	2
1280.3.r	\(\chi_{1280}(191, \cdot)\)	n/a	128	2
1280.3.t	\(\chi_{1280}(193, \cdot)\)	n/a	192	2
1280.3.v	\(\chi_{1280}(33, \cdot)\)	n/a	368	4
1280.3.w	\(\chi_{1280}(31, \cdot)\)	n/a	256	4
1280.3.y	\(\chi_{1280}(159, \cdot)\)	n/a	368	4
1280.3.bb	\(\chi_{1280}(353, \cdot)\)	n/a	368	4
1280.3.bc	\(\chi_{1280}(17, \cdot)\)	n/a	752	8
1280.3.bg	\(\chi_{1280}(111, \cdot)\)	n/a	512	8
1280.3.bh	\(\chi_{1280}(79, \cdot)\)	n/a	752	8
1280.3.bi	\(\chi_{1280}(177, \cdot)\)	n/a	752	8
1280.3.bk	\(\chi_{1280}(57, \cdot)\)	None	0	16
1280.3.bn	\(\chi_{1280}(39, \cdot)\)	None	0	16
1280.3.bp	\(\chi_{1280}(71, \cdot)\)	None	0	16
1280.3.bq	\(\chi_{1280}(137, \cdot)\)	None	0	16
1280.3.bs	\(\chi_{1280}(53, \cdot)\)	n/a	12224	32
1280.3.bu	\(\chi_{1280}(19, \cdot)\)	n/a	12224	32
1280.3.bx	\(\chi_{1280}(11, \cdot)\)	n/a	8192	32
1280.3.bz	\(\chi_{1280}(13, \cdot)\)	n/a	12224	32

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1280))\) into lower level spaces

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