Space of modular forms of level 480 and weight 2

• Label: 480.2
• Level: 480
• Weight: 2
• Dimension: 2316
• Nonzero newspaces: 20
• Newform subspaces: 48
• Sturm bound: 24576
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 48 \)
Sturm bound:			\(24576\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(480))\).

	Total	New	Old
Modular forms	6656	2436	4220
Cusp forms	5633	2316	3317
Eisenstein series	1023	120	903

Trace form

2316 * q - 8 * q^3 - 16 * q^4 - 4 * q^5 - 24 * q^6 - 16 * q^7 - 20 * q^9 - 8 * q^10 + 24 * q^12 + 8 * q^13 + 64 * q^14 + 32 * q^16 + 32 * q^17 + 8 * q^18 + 8 * q^19 + 32 * q^20 + 8 * q^21 + 32 * q^22 + 48 * q^23 - 32 * q^24 - 28 * q^25 - 80 * q^26 + 64 * q^27 - 96 * q^28 + 8 * q^29 - 60 * q^30 + 88 * q^31 - 80 * q^32 + 8 * q^33 - 64 * q^34 + 96 * q^35 - 128 * q^36 + 24 * q^37 - 80 * q^38 + 56 * q^39 - 64 * q^40 + 48 * q^41 - 128 * q^42 + 48 * q^43 - 16 * q^44 - 32 * q^45 - 48 * q^46 - 112 * q^48 - 28 * q^49 - 24 * q^50 - 40 * q^51 - 112 * q^52 + 40 * q^53 - 112 * q^54 - 40 * q^55 - 112 * q^56 - 80 * q^57 - 160 * q^58 - 128 * q^59 - 136 * q^60 + 72 * q^61 - 96 * q^62 - 64 * q^63 - 256 * q^64 - 72 * q^65 - 200 * q^66 - 160 * q^67 - 208 * q^68 + 24 * q^69 - 336 * q^70 - 144 * q^71 - 128 * q^72 - 72 * q^73 - 288 * q^74 - 76 * q^75 - 304 * q^76 - 64 * q^77 - 184 * q^78 - 136 * q^79 - 264 * q^80 - 68 * q^81 - 176 * q^82 - 80 * q^83 - 48 * q^84 - 152 * q^85 - 128 * q^86 - 208 * q^87 - 192 * q^88 - 128 * q^89 - 120 * q^90 - 96 * q^91 - 128 * q^92 - 128 * q^93 - 64 * q^94 - 64 * q^95 + 128 * q^96 - 88 * q^97 + 64 * q^98 - 232 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)

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
480.2.a	\(\chi_{480}(1, \cdot)\)	480.2.a.a	1	1
		480.2.a.b	1
		480.2.a.c	1
		480.2.a.d	1
		480.2.a.e	1
		480.2.a.f	1
		480.2.a.g	1
		480.2.a.h	1
480.2.b	\(\chi_{480}(431, \cdot)\)	480.2.b.a	8	1
		480.2.b.b	8
480.2.d	\(\chi_{480}(49, \cdot)\)	480.2.d.a	6	1
		480.2.d.b	6
480.2.f	\(\chi_{480}(289, \cdot)\)	480.2.f.a	2	1
		480.2.f.b	2
		480.2.f.c	2
		480.2.f.d	2
		480.2.f.e	4
480.2.h	\(\chi_{480}(191, \cdot)\)	480.2.h.a	4	1
		480.2.h.b	4
		480.2.h.c	4
		480.2.h.d	4
480.2.k	\(\chi_{480}(241, \cdot)\)	480.2.k.a	2	1
		480.2.k.b	6
480.2.m	\(\chi_{480}(239, \cdot)\)	480.2.m.a	4	1
		480.2.m.b	16
480.2.o	\(\chi_{480}(479, \cdot)\)	480.2.o.a	24	1
480.2.s	\(\chi_{480}(121, \cdot)\)	None	0	2
480.2.t	\(\chi_{480}(119, \cdot)\)	None	0	2
480.2.v	\(\chi_{480}(257, \cdot)\)	480.2.v.a	4	2
		480.2.v.b	4
		480.2.v.c	16
		480.2.v.d	24
480.2.w	\(\chi_{480}(127, \cdot)\)	480.2.w.a	4	2
		480.2.w.b	4
		480.2.w.c	8
		480.2.w.d	8
480.2.y	\(\chi_{480}(7, \cdot)\)	None	0	2
480.2.bb	\(\chi_{480}(233, \cdot)\)	None	0	2
480.2.bc	\(\chi_{480}(103, \cdot)\)	None	0	2
480.2.bf	\(\chi_{480}(137, \cdot)\)	None	0	2
480.2.bh	\(\chi_{480}(367, \cdot)\)	480.2.bh.a	24	2
480.2.bi	\(\chi_{480}(17, \cdot)\)	480.2.bi.a	4	2
		480.2.bi.b	4
		480.2.bi.c	32
480.2.bk	\(\chi_{480}(71, \cdot)\)	None	0	2
480.2.bl	\(\chi_{480}(169, \cdot)\)	None	0	2
480.2.bo	\(\chi_{480}(43, \cdot)\)	480.2.bo.a	192	4
480.2.br	\(\chi_{480}(173, \cdot)\)	480.2.br.a	368	4
480.2.bs	\(\chi_{480}(59, \cdot)\)	480.2.bs.a	16	4
		480.2.bs.b	352
480.2.bv	\(\chi_{480}(61, \cdot)\)	480.2.bv.a	56	4
		480.2.bv.b	72
480.2.bx	\(\chi_{480}(11, \cdot)\)	480.2.bx.a	256	4
480.2.by	\(\chi_{480}(109, \cdot)\)	480.2.by.a	192	4
480.2.cb	\(\chi_{480}(53, \cdot)\)	480.2.cb.a	368	4
480.2.cc	\(\chi_{480}(163, \cdot)\)	480.2.cc.a	192	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(480))\) into lower level spaces

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