Space of modular forms of level 280 and weight 2

• Label: 280.2
• Level: 280
• Weight: 2
• Dimension: 1078
• Nonzero newspaces: 18
• Newform subspaces: 44
• Sturm bound: 9216
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 44 \)
Sturm bound:			\(9216\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(280))\).

	Total	New	Old
Modular forms	2592	1198	1394
Cusp forms	2017	1078	939
Eisenstein series	575	120	455

Trace form

1078 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 2 * q^5 - 20 * q^6 - 4 * q^7 - 16 * q^8 + 14 * q^9 - 10 * q^10 - 28 * q^12 + 16 * q^13 - 20 * q^14 - 32 * q^15 - 52 * q^16 - 96 * q^18 - 36 * q^19 - 68 * q^20 - 8 * q^21 - 116 * q^22 - 48 * q^23 - 132 * q^24 - 28 * q^25 - 112 * q^26 - 88 * q^27 - 100 * q^28 + 12 * q^29 - 66 * q^30 - 72 * q^31 - 24 * q^32 - 20 * q^33 - 12 * q^34 - 26 * q^35 - 52 * q^36 - 40 * q^39 + 40 * q^40 + 12 * q^41 + 84 * q^42 - 64 * q^43 + 68 * q^44 + 8 * q^45 + 88 * q^46 - 96 * q^47 + 124 * q^48 - 50 * q^49 - 56 * q^50 - 136 * q^51 + 56 * q^52 - 24 * q^53 + 84 * q^54 - 128 * q^55 - 176 * q^57 - 40 * q^58 - 172 * q^59 - 32 * q^60 - 28 * q^61 - 16 * q^62 - 172 * q^63 - 4 * q^64 - 136 * q^65 - 20 * q^66 - 104 * q^67 - 52 * q^68 - 136 * q^69 - 42 * q^70 - 144 * q^71 - 24 * q^72 - 136 * q^73 - 140 * q^74 + 8 * q^75 - 180 * q^76 - 92 * q^77 - 64 * q^78 + 16 * q^79 - 84 * q^80 - 198 * q^81 - 84 * q^82 - 12 * q^83 - 196 * q^84 - 52 * q^85 - 268 * q^86 - 24 * q^87 - 156 * q^88 - 64 * q^89 - 88 * q^90 + 4 * q^91 - 148 * q^92 - 12 * q^93 - 148 * q^94 + 12 * q^95 - 180 * q^96 - 92 * q^97 - 100 * q^98 + 128 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)

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
280.2.a	\(\chi_{280}(1, \cdot)\)	280.2.a.a	1	1
		280.2.a.b	1
		280.2.a.c	2
		280.2.a.d	2
280.2.b	\(\chi_{280}(141, \cdot)\)	280.2.b.a	2	1
		280.2.b.b	2
		280.2.b.c	8
		280.2.b.d	12
280.2.e	\(\chi_{280}(279, \cdot)\)	None	0	1
280.2.g	\(\chi_{280}(169, \cdot)\)	280.2.g.a	2	1
		280.2.g.b	6
280.2.h	\(\chi_{280}(251, \cdot)\)	280.2.h.a	16	1
		280.2.h.b	16
280.2.k	\(\chi_{280}(111, \cdot)\)	None	0	1
280.2.l	\(\chi_{280}(29, \cdot)\)	280.2.l.a	36	1
280.2.n	\(\chi_{280}(139, \cdot)\)	280.2.n.a	4	1
		280.2.n.b	40
280.2.q	\(\chi_{280}(81, \cdot)\)	280.2.q.a	2	2
		280.2.q.b	2
		280.2.q.c	2
		280.2.q.d	4
		280.2.q.e	6
280.2.s	\(\chi_{280}(13, \cdot)\)	280.2.s.a	8	2
		280.2.s.b	8
		280.2.s.c	72
280.2.t	\(\chi_{280}(127, \cdot)\)	None	0	2
280.2.w	\(\chi_{280}(43, \cdot)\)	280.2.w.a	72	2
280.2.x	\(\chi_{280}(97, \cdot)\)	280.2.x.a	24	2
280.2.ba	\(\chi_{280}(19, \cdot)\)	280.2.ba.a	8	2
		280.2.ba.b	80
280.2.bc	\(\chi_{280}(31, \cdot)\)	None	0	2
280.2.bf	\(\chi_{280}(109, \cdot)\)	280.2.bf.a	88	2
280.2.bg	\(\chi_{280}(9, \cdot)\)	280.2.bg.a	24	2
280.2.bj	\(\chi_{280}(131, \cdot)\)	280.2.bj.a	4	2
		280.2.bj.b	4
		280.2.bj.c	4
		280.2.bj.d	4
		280.2.bj.e	24
		280.2.bj.f	24
280.2.bl	\(\chi_{280}(221, \cdot)\)	280.2.bl.a	4	2
		280.2.bl.b	60
280.2.bm	\(\chi_{280}(159, \cdot)\)	None	0	2
280.2.bo	\(\chi_{280}(17, \cdot)\)	280.2.bo.a	48	4
280.2.br	\(\chi_{280}(67, \cdot)\)	280.2.br.a	176	4
280.2.bs	\(\chi_{280}(23, \cdot)\)	None	0	4
280.2.bv	\(\chi_{280}(117, \cdot)\)	280.2.bv.a	4	4
		280.2.bv.b	4
		280.2.bv.c	4
		280.2.bv.d	4
		280.2.bv.e	160

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(280))\) into lower level spaces

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