Space of modular forms of level 280 and weight 10

• Label: 280.10
• Level: 280
• Weight: 10
• Dimension: 10190
• Nonzero newspaces: 18
• Sturm bound: 46080
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(46080\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(280))\).

	Total	New	Old
Modular forms	21024	10310	10714
Cusp forms	20448	10190	10258
Eisenstein series	576	120	456

Trace form

10190 * q - 76 * q^2 + 28 * q^3 - 1716 * q^4 - 3526 * q^5 + 18716 * q^6 + 11644 * q^7 - 13552 * q^8 - 115050 * q^9 + 52774 * q^10 + 105600 * q^11 + 61572 * q^12 + 33872 * q^13 - 736172 * q^14 - 633184 * q^15 + 2891276 * q^16 - 408288 * q^17 - 3208552 * q^18 + 507292 * q^19 + 137140 * q^20 - 6518216 * q^21 - 5472012 * q^22 + 22627344 * q^23 + 5484476 * q^24 + 17304236 * q^25 - 16659448 * q^26 - 27704792 * q^27 - 9477060 * q^28 + 27975132 * q^29 - 47244802 * q^30 - 16903848 * q^31 + 34036584 * q^32 - 39143412 * q^33 - 57913484 * q^34 + 32802070 * q^35 + 123640012 * q^36 - 13530784 * q^37 - 21169560 * q^38 - 370272264 * q^39 - 42348376 * q^40 + 122057052 * q^41 + 311105092 * q^42 + 501306848 * q^43 - 20678428 * q^44 - 159137600 * q^45 - 251345904 * q^46 - 707257344 * q^47 - 196027908 * q^48 - 517785770 * q^49 - 398818664 * q^50 + 1308131288 * q^51 + 308287720 * q^52 - 248241528 * q^53 + 740408348 * q^54 - 607778368 * q^55 + 102127008 * q^56 + 514637712 * q^57 + 392371336 * q^58 + 812826356 * q^59 - 1397342192 * q^60 + 408096244 * q^61 - 2056281352 * q^62 + 99424308 * q^63 + 1346338044 * q^64 + 1113291848 * q^65 + 4240958980 * q^66 - 618456072 * q^67 + 2004967340 * q^68 + 866651192 * q^69 - 1721442914 * q^70 - 374623248 * q^71 - 5331612664 * q^72 + 1155957048 * q^73 - 707169116 * q^74 + 1137288 * q^75 + 1905721772 * q^76 + 2834082628 * q^77 + 11608592128 * q^78 + 3974363792 * q^79 + 4383100236 * q^80 - 6537519726 * q^81 - 9558544500 * q^82 - 7595243244 * q^83 - 13233298020 * q^84 + 4837923692 * q^85 - 4487310220 * q^86 - 2644670840 * q^87 + 6020849252 * q^88 + 5016171728 * q^89 + 11020606632 * q^90 + 6251175044 * q^91 + 10741640348 * q^92 - 2027023916 * q^93 - 1636005044 * q^94 - 12929775828 * q^95 - 14930879156 * q^96 - 5969900348 * q^97 + 780831116 * q^98 + 11840687712 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(280))\)

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
280.10.a	\(\chi_{280}(1, \cdot)\)	280.10.a.a	6	1
		280.10.a.b	6
		280.10.a.c	6
		280.10.a.d	6
		280.10.a.e	7
		280.10.a.f	7
		280.10.a.g	8
		280.10.a.h	8
280.10.b	\(\chi_{280}(141, \cdot)\)	n/a	216	1
280.10.e	\(\chi_{280}(279, \cdot)\)	None	0	1
280.10.g	\(\chi_{280}(169, \cdot)\)	280.10.g.a	38	1
		280.10.g.b	42
280.10.h	\(\chi_{280}(251, \cdot)\)	n/a	288	1
280.10.k	\(\chi_{280}(111, \cdot)\)	None	0	1
280.10.l	\(\chi_{280}(29, \cdot)\)	n/a	324	1
280.10.n	\(\chi_{280}(139, \cdot)\)	n/a	428	1
280.10.q	\(\chi_{280}(81, \cdot)\)	n/a	144	2
280.10.s	\(\chi_{280}(13, \cdot)\)	n/a	856	2
280.10.t	\(\chi_{280}(127, \cdot)\)	None	0	2
280.10.w	\(\chi_{280}(43, \cdot)\)	n/a	648	2
280.10.x	\(\chi_{280}(97, \cdot)\)	n/a	216	2
280.10.ba	\(\chi_{280}(19, \cdot)\)	n/a	856	2
280.10.bc	\(\chi_{280}(31, \cdot)\)	None	0	2
280.10.bf	\(\chi_{280}(109, \cdot)\)	n/a	856	2
280.10.bg	\(\chi_{280}(9, \cdot)\)	n/a	216	2
280.10.bj	\(\chi_{280}(131, \cdot)\)	n/a	576	2
280.10.bl	\(\chi_{280}(221, \cdot)\)	n/a	576	2
280.10.bm	\(\chi_{280}(159, \cdot)\)	None	0	2
280.10.bo	\(\chi_{280}(17, \cdot)\)	n/a	432	4
280.10.br	\(\chi_{280}(67, \cdot)\)	n/a	1712	4
280.10.bs	\(\chi_{280}(23, \cdot)\)	None	0	4
280.10.bv	\(\chi_{280}(117, \cdot)\)	n/a	1712	4

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(280))\) into lower level spaces

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