Space of modular forms of level 480 and weight 4

• Label: 480.4
• Level: 480
• Weight: 4
• Dimension: 7068
• Nonzero newspaces: 20
• Sturm bound: 49152
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(49152\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(480))\).

	Total	New	Old
Modular forms	18944	7188	11756
Cusp forms	17920	7068	10852
Eisenstein series	1024	120	904

Trace form

7068 * q - 8 * q^3 - 16 * q^4 + 4 * q^5 - 24 * q^6 + 48 * q^7 + 28 * q^9 + 216 * q^10 - 104 * q^12 - 488 * q^13 - 832 * q^14 - 64 * q^15 - 1248 * q^16 - 416 * q^17 - 152 * q^18 - 56 * q^19 + 160 * q^20 - 56 * q^21 + 768 * q^22 + 1968 * q^23 - 96 * q^24 + 52 * q^25 + 80 * q^26 - 800 * q^27 + 1504 * q^28 + 568 * q^29 + 1116 * q^30 - 3240 * q^31 + 2480 * q^32 - 8 * q^33 + 2112 * q^34 - 1824 * q^35 - 1184 * q^36 - 1336 * q^37 - 880 * q^38 + 568 * q^39 - 1664 * q^40 - 240 * q^41 - 1808 * q^42 + 2352 * q^43 - 2000 * q^44 + 424 * q^45 - 48 * q^46 + 4880 * q^48 + 1844 * q^49 - 2856 * q^50 + 216 * q^51 - 6640 * q^52 + 5720 * q^53 + 1432 * q^55 + 784 * q^56 + 1312 * q^57 + 4736 * q^58 + 5504 * q^59 - 1384 * q^60 - 5608 * q^61 + 5856 * q^62 + 128 * q^63 + 4352 * q^64 - 6360 * q^65 - 1208 * q^66 + 1184 * q^67 - 1808 * q^68 - 7720 * q^69 - 384 * q^70 - 2064 * q^71 + 2752 * q^72 - 4904 * q^73 + 3360 * q^74 - 620 * q^75 - 3376 * q^76 + 13888 * q^77 + 9704 * q^78 - 5128 * q^79 + 13944 * q^80 + 1740 * q^81 + 11664 * q^82 + 5360 * q^83 + 13104 * q^84 + 11000 * q^85 + 4736 * q^86 + 5840 * q^87 + 1216 * q^88 - 1408 * q^89 - 10272 * q^90 + 2912 * q^91 - 6784 * q^92 + 128 * q^93 + 3904 * q^94 - 2624 * q^95 - 14976 * q^96 + 840 * q^97 - 4672 * q^98 + 13016 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(480))\)

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
480.4.a	\(\chi_{480}(1, \cdot)\)	480.4.a.a	1	1
		480.4.a.b	1
		480.4.a.c	1
		480.4.a.d	1
		480.4.a.e	1
		480.4.a.f	1
		480.4.a.g	1
		480.4.a.h	1
		480.4.a.i	1
		480.4.a.j	1
		480.4.a.k	1
		480.4.a.l	1
		480.4.a.m	2
		480.4.a.n	2
		480.4.a.o	2
		480.4.a.p	2
		480.4.a.q	2
		480.4.a.r	2
480.4.b	\(\chi_{480}(431, \cdot)\)	480.4.b.a	24	1
		480.4.b.b	24
480.4.d	\(\chi_{480}(49, \cdot)\)	480.4.d.a	18	1
		480.4.d.b	18
480.4.f	\(\chi_{480}(289, \cdot)\)	480.4.f.a	2	1
		480.4.f.b	2
		480.4.f.c	4
		480.4.f.d	6
		480.4.f.e	6
		480.4.f.f	8
		480.4.f.g	8
480.4.h	\(\chi_{480}(191, \cdot)\)	480.4.h.a	24	1
		480.4.h.b	24
480.4.k	\(\chi_{480}(241, \cdot)\)	480.4.k.a	2	1
		480.4.k.b	8
		480.4.k.c	14
480.4.m	\(\chi_{480}(239, \cdot)\)	480.4.m.a	4	1
		480.4.m.b	64
480.4.o	\(\chi_{480}(479, \cdot)\)	480.4.o.a	72	1
480.4.s	\(\chi_{480}(121, \cdot)\)	None	0	2
480.4.t	\(\chi_{480}(119, \cdot)\)	None	0	2
480.4.v	\(\chi_{480}(257, \cdot)\)	n/a	144	2
480.4.w	\(\chi_{480}(127, \cdot)\)	480.4.w.a	16	2
		480.4.w.b	16
		480.4.w.c	20
		480.4.w.d	20
480.4.y	\(\chi_{480}(7, \cdot)\)	None	0	2
480.4.bb	\(\chi_{480}(233, \cdot)\)	None	0	2
480.4.bc	\(\chi_{480}(103, \cdot)\)	None	0	2
480.4.bf	\(\chi_{480}(137, \cdot)\)	None	0	2
480.4.bh	\(\chi_{480}(367, \cdot)\)	480.4.bh.a	72	2
480.4.bi	\(\chi_{480}(17, \cdot)\)	n/a	136	2
480.4.bk	\(\chi_{480}(71, \cdot)\)	None	0	2
480.4.bl	\(\chi_{480}(169, \cdot)\)	None	0	2
480.4.bo	\(\chi_{480}(43, \cdot)\)	n/a	576	4
480.4.br	\(\chi_{480}(173, \cdot)\)	n/a	1136	4
480.4.bs	\(\chi_{480}(59, \cdot)\)	n/a	1136	4
480.4.bv	\(\chi_{480}(61, \cdot)\)	n/a	384	4
480.4.bx	\(\chi_{480}(11, \cdot)\)	n/a	768	4
480.4.by	\(\chi_{480}(109, \cdot)\)	n/a	576	4
480.4.cb	\(\chi_{480}(53, \cdot)\)	n/a	1136	4
480.4.cc	\(\chi_{480}(163, \cdot)\)	n/a	576	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(480))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(480)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)