Space of modular forms of level 520 and weight 2

• Label: 520.2
• Level: 520
• Weight: 2
• Dimension: 3976
• Nonzero newspaces: 32
• Newform subspaces: 78
• Sturm bound: 32256
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Newform subspaces:			\( 78 \)
Sturm bound:			\(32256\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(520))\).

	Total	New	Old
Modular forms	8640	4240	4400
Cusp forms	7489	3976	3513
Eisenstein series	1151	264	887

Trace form

3976 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 + 2 * q^5 - 56 * q^6 - 8 * q^7 - 16 * q^8 - 22 * q^9 - 28 * q^10 - 48 * q^11 - 40 * q^12 + 2 * q^13 - 64 * q^14 - 44 * q^15 - 88 * q^16 - 30 * q^17 - 72 * q^18 - 24 * q^19 - 68 * q^20 + 32 * q^21 - 56 * q^22 - 72 * q^24 - 46 * q^25 - 80 * q^26 + 8 * q^27 - 8 * q^28 + 42 * q^29 - 36 * q^30 - 48 * q^31 + 24 * q^32 + 16 * q^33 + 48 * q^34 - 40 * q^35 - 64 * q^36 - 6 * q^37 + 24 * q^38 - 56 * q^39 - 32 * q^40 - 126 * q^41 - 120 * q^42 - 160 * q^43 - 112 * q^44 - 43 * q^45 - 248 * q^46 - 144 * q^47 - 200 * q^48 - 86 * q^49 - 176 * q^50 - 256 * q^51 - 260 * q^52 - 84 * q^53 - 288 * q^54 - 164 * q^55 - 384 * q^56 - 104 * q^57 - 304 * q^58 - 136 * q^59 - 236 * q^60 - 46 * q^61 - 256 * q^62 - 56 * q^63 - 232 * q^64 - 59 * q^65 - 272 * q^66 + 40 * q^67 - 64 * q^68 + 56 * q^69 - 96 * q^70 + 72 * q^71 - 4 * q^73 + 16 * q^74 + 140 * q^75 - 72 * q^76 + 128 * q^77 + 40 * q^78 + 160 * q^79 + 12 * q^80 - 54 * q^81 + 48 * q^82 + 216 * q^83 + 208 * q^84 + 35 * q^85 + 8 * q^86 + 24 * q^87 + 96 * q^88 - 76 * q^89 + 128 * q^90 - 200 * q^91 + 128 * q^92 - 72 * q^93 + 104 * q^94 - 108 * q^95 + 264 * q^96 - 92 * q^97 + 168 * q^98 - 400 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)

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
520.2.a	\(\chi_{520}(1, \cdot)\)	520.2.a.a	1	1
		520.2.a.b	1
		520.2.a.c	2
		520.2.a.d	2
		520.2.a.e	2
		520.2.a.f	2
		520.2.a.g	2
520.2.d	\(\chi_{520}(209, \cdot)\)	520.2.d.a	2	1
		520.2.d.b	6
		520.2.d.c	10
520.2.e	\(\chi_{520}(181, \cdot)\)	520.2.e.a	28	1
		520.2.e.b	28
520.2.f	\(\chi_{520}(129, \cdot)\)	520.2.f.a	10	1
		520.2.f.b	10
520.2.g	\(\chi_{520}(261, \cdot)\)	520.2.g.a	24	1
		520.2.g.b	24
520.2.j	\(\chi_{520}(469, \cdot)\)	520.2.j.a	36	1
		520.2.j.b	36
520.2.k	\(\chi_{520}(441, \cdot)\)	520.2.k.a	6	1
		520.2.k.b	8
520.2.p	\(\chi_{520}(389, \cdot)\)	520.2.p.a	8	1
		520.2.p.b	72
520.2.q	\(\chi_{520}(81, \cdot)\)	520.2.q.a	2	2
		520.2.q.b	2
		520.2.q.c	2
		520.2.q.d	2
		520.2.q.e	2
		520.2.q.f	4
		520.2.q.g	6
		520.2.q.h	8
520.2.s	\(\chi_{520}(31, \cdot)\)	None	0	2
520.2.t	\(\chi_{520}(99, \cdot)\)	520.2.t.a	4	2
		520.2.t.b	4
		520.2.t.c	152
520.2.w	\(\chi_{520}(57, \cdot)\)	520.2.w.a	2	2
		520.2.w.b	2
		520.2.w.c	2
		520.2.w.d	4
		520.2.w.e	12
		520.2.w.f	20
520.2.y	\(\chi_{520}(317, \cdot)\)	520.2.y.a	160	2
520.2.bb	\(\chi_{520}(183, \cdot)\)	None	0	2
520.2.bc	\(\chi_{520}(363, \cdot)\)	520.2.bc.a	12	2
		520.2.bc.b	12
		520.2.bc.c	136
520.2.bd	\(\chi_{520}(103, \cdot)\)	None	0	2
520.2.be	\(\chi_{520}(27, \cdot)\)	520.2.be.a	144	2
520.2.bh	\(\chi_{520}(177, \cdot)\)	520.2.bh.a	2	2
		520.2.bh.b	2
		520.2.bh.c	2
		520.2.bh.d	4
		520.2.bh.e	12
		520.2.bh.f	20
520.2.bj	\(\chi_{520}(213, \cdot)\)	520.2.bj.a	160	2
520.2.bm	\(\chi_{520}(291, \cdot)\)	520.2.bm.a	112	2
520.2.bn	\(\chi_{520}(239, \cdot)\)	None	0	2
520.2.bp	\(\chi_{520}(69, \cdot)\)	520.2.bp.a	160	2
520.2.bu	\(\chi_{520}(121, \cdot)\)	520.2.bu.a	12	2
		520.2.bu.b	16
520.2.bv	\(\chi_{520}(29, \cdot)\)	520.2.bv.a	160	2
520.2.by	\(\chi_{520}(61, \cdot)\)	520.2.by.a	4	2
		520.2.by.b	4
		520.2.by.c	104
520.2.bz	\(\chi_{520}(49, \cdot)\)	520.2.bz.a	20	2
		520.2.bz.b	20
520.2.ca	\(\chi_{520}(101, \cdot)\)	520.2.ca.a	56	2
		520.2.ca.b	56
520.2.cb	\(\chi_{520}(9, \cdot)\)	520.2.cb.a	44	2
520.2.cf	\(\chi_{520}(119, \cdot)\)	None	0	4
520.2.cg	\(\chi_{520}(11, \cdot)\)	520.2.cg.a	224	4
520.2.cj	\(\chi_{520}(37, \cdot)\)	520.2.cj.a	320	4
520.2.cl	\(\chi_{520}(137, \cdot)\)	520.2.cl.a	4	4
		520.2.cl.b	40
		520.2.cl.c	40
520.2.cm	\(\chi_{520}(3, \cdot)\)	520.2.cm.a	320	4
520.2.cn	\(\chi_{520}(23, \cdot)\)	None	0	4
520.2.cs	\(\chi_{520}(43, \cdot)\)	520.2.cs.a	320	4
520.2.ct	\(\chi_{520}(87, \cdot)\)	None	0	4
520.2.cu	\(\chi_{520}(197, \cdot)\)	520.2.cu.a	320	4
520.2.cw	\(\chi_{520}(33, \cdot)\)	520.2.cw.a	4	4
		520.2.cw.b	40
		520.2.cw.c	40
520.2.cz	\(\chi_{520}(19, \cdot)\)	520.2.cz.a	8	4
		520.2.cz.b	8
		520.2.cz.c	304
520.2.da	\(\chi_{520}(71, \cdot)\)	None	0	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 2}\)