Space of modular forms of level 720 and weight 2

• Label: 720.2
• Level: 720
• Weight: 2
• Dimension: 5522
• Nonzero newspaces: 28
• Newform subspaces: 120
• Sturm bound: 55296
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Newform subspaces:			\( 120 \)
Sturm bound:			\(55296\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(720))\).

	Total	New	Old
Modular forms	14720	5764	8956
Cusp forms	12929	5522	7407
Eisenstein series	1791	242	1549

Trace form

5522 * q - 12 * q^2 - 12 * q^3 - 16 * q^4 - 25 * q^5 - 48 * q^6 - 20 * q^7 - 24 * q^8 - 12 * q^9 - 56 * q^10 - 54 * q^11 - 16 * q^12 - 36 * q^13 + 24 * q^14 - 21 * q^15 + 8 * q^16 - 18 * q^17 + 24 * q^18 - 44 * q^19 + 32 * q^20 - 34 * q^21 + 80 * q^22 + 20 * q^23 + 48 * q^24 + 19 * q^25 + 80 * q^26 + 24 * q^27 + 72 * q^28 + 54 * q^29 - 4 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 72 * q^34 + 72 * q^35 - 40 * q^36 - 22 * q^37 - 48 * q^38 + 102 * q^39 + 4 * q^40 + 50 * q^41 - 96 * q^42 + 124 * q^43 - 128 * q^44 + 13 * q^45 - 168 * q^46 + 180 * q^47 - 120 * q^48 - 16 * q^49 - 52 * q^50 + 76 * q^51 - 104 * q^52 + 82 * q^53 - 104 * q^54 + 106 * q^55 - 240 * q^56 + 16 * q^57 - 88 * q^58 + 142 * q^59 - 132 * q^60 + 50 * q^61 - 216 * q^62 + 54 * q^63 + 80 * q^64 - 35 * q^65 - 288 * q^66 + 100 * q^67 - 240 * q^68 - 122 * q^69 - 52 * q^70 - 12 * q^71 - 240 * q^72 + 66 * q^73 - 216 * q^74 - 31 * q^75 - 32 * q^76 - 38 * q^77 - 264 * q^78 - 6 * q^79 - 232 * q^80 - 260 * q^81 - 120 * q^82 - 128 * q^83 - 304 * q^84 + 12 * q^85 - 392 * q^86 - 162 * q^87 - 248 * q^88 - 68 * q^89 - 168 * q^90 - 216 * q^91 - 376 * q^92 + 74 * q^93 - 264 * q^94 - 112 * q^95 - 184 * q^96 - 32 * q^97 - 388 * q^98 - 78 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)

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
720.2.a	\(\chi_{720}(1, \cdot)\)	720.2.a.a	1	1
		720.2.a.b	1
		720.2.a.c	1
		720.2.a.d	1
		720.2.a.e	1
		720.2.a.f	1
		720.2.a.g	1
		720.2.a.h	1
		720.2.a.i	1
		720.2.a.j	1
720.2.b	\(\chi_{720}(71, \cdot)\)	None	0	1
720.2.d	\(\chi_{720}(649, \cdot)\)	None	0	1
720.2.f	\(\chi_{720}(289, \cdot)\)	720.2.f.a	2	1
		720.2.f.b	2
		720.2.f.c	2
		720.2.f.d	2
		720.2.f.e	2
		720.2.f.f	2
		720.2.f.g	2
720.2.h	\(\chi_{720}(431, \cdot)\)	720.2.h.a	8	1
720.2.k	\(\chi_{720}(361, \cdot)\)	None	0	1
720.2.m	\(\chi_{720}(359, \cdot)\)	None	0	1
720.2.o	\(\chi_{720}(719, \cdot)\)	720.2.o.a	4	1
		720.2.o.b	8
720.2.q	\(\chi_{720}(241, \cdot)\)	720.2.q.a	2	2
		720.2.q.b	2
		720.2.q.c	2
		720.2.q.d	2
		720.2.q.e	2
		720.2.q.f	4
		720.2.q.g	4
		720.2.q.h	4
		720.2.q.i	6
		720.2.q.j	6
		720.2.q.k	6
		720.2.q.l	8
720.2.t	\(\chi_{720}(181, \cdot)\)	720.2.t.a	4	2
		720.2.t.b	8
		720.2.t.c	16
		720.2.t.d	20
		720.2.t.e	32
720.2.u	\(\chi_{720}(179, \cdot)\)	720.2.u.a	96	2
720.2.w	\(\chi_{720}(17, \cdot)\)	720.2.w.a	4	2
		720.2.w.b	4
		720.2.w.c	4
		720.2.w.d	4
		720.2.w.e	8
720.2.x	\(\chi_{720}(127, \cdot)\)	720.2.x.a	2	2
		720.2.x.b	2
		720.2.x.c	2
		720.2.x.d	4
		720.2.x.e	4
		720.2.x.f	8
		720.2.x.g	8
720.2.z	\(\chi_{720}(163, \cdot)\)	720.2.z.a	2	2
		720.2.z.b	2
		720.2.z.c	2
		720.2.z.d	2
		720.2.z.e	6
		720.2.z.f	16
		720.2.z.g	18
		720.2.z.h	20
		720.2.z.i	48
720.2.bc	\(\chi_{720}(197, \cdot)\)	720.2.bc.a	96	2
720.2.bd	\(\chi_{720}(307, \cdot)\)	720.2.bd.a	2	2
		720.2.bd.b	2
		720.2.bd.c	2
		720.2.bd.d	2
		720.2.bd.e	6
		720.2.bd.f	16
		720.2.bd.g	18
		720.2.bd.h	20
		720.2.bd.i	48
720.2.bg	\(\chi_{720}(53, \cdot)\)	720.2.bg.a	96	2
720.2.bi	\(\chi_{720}(343, \cdot)\)	None	0	2
720.2.bj	\(\chi_{720}(233, \cdot)\)	None	0	2
720.2.bl	\(\chi_{720}(251, \cdot)\)	720.2.bl.a	8	2
		720.2.bl.b	24
		720.2.bl.c	32
720.2.bm	\(\chi_{720}(109, \cdot)\)	720.2.bm.a	2	2
		720.2.bm.b	2
		720.2.bm.c	4
		720.2.bm.d	4
		720.2.bm.e	8
		720.2.bm.f	16
		720.2.bm.g	32
		720.2.bm.h	48
720.2.br	\(\chi_{720}(239, \cdot)\)	720.2.br.a	8	2
		720.2.br.b	16
		720.2.br.c	24
		720.2.br.d	24
720.2.bt	\(\chi_{720}(119, \cdot)\)	None	0	2
720.2.bv	\(\chi_{720}(121, \cdot)\)	None	0	2
720.2.bw	\(\chi_{720}(191, \cdot)\)	720.2.bw.a	16	2
		720.2.bw.b	16
		720.2.bw.c	16
720.2.by	\(\chi_{720}(49, \cdot)\)	720.2.by.a	4	2
		720.2.by.b	4
		720.2.by.c	8
		720.2.by.d	8
		720.2.by.e	12
		720.2.by.f	32
720.2.ca	\(\chi_{720}(169, \cdot)\)	None	0	2
720.2.cc	\(\chi_{720}(311, \cdot)\)	None	0	2
720.2.ce	\(\chi_{720}(229, \cdot)\)	720.2.ce.a	560	4
720.2.cf	\(\chi_{720}(11, \cdot)\)	720.2.cf.a	384	4
720.2.ci	\(\chi_{720}(7, \cdot)\)	None	0	4
720.2.cl	\(\chi_{720}(137, \cdot)\)	None	0	4
720.2.cm	\(\chi_{720}(77, \cdot)\)	720.2.cm.a	560	4
720.2.cp	\(\chi_{720}(43, \cdot)\)	720.2.cp.a	4	4
		720.2.cp.b	4
		720.2.cp.c	552
720.2.cq	\(\chi_{720}(173, \cdot)\)	720.2.cq.a	560	4
720.2.ct	\(\chi_{720}(187, \cdot)\)	720.2.ct.a	4	4
		720.2.ct.b	4
		720.2.ct.c	552
720.2.cu	\(\chi_{720}(113, \cdot)\)	720.2.cu.a	8	4
		720.2.cu.b	16
		720.2.cu.c	16
		720.2.cu.d	24
		720.2.cu.e	72
720.2.cx	\(\chi_{720}(223, \cdot)\)	720.2.cx.a	8	4
		720.2.cx.b	8
		720.2.cx.c	40
		720.2.cx.d	40
		720.2.cx.e	48
720.2.da	\(\chi_{720}(59, \cdot)\)	720.2.da.a	4	4
		720.2.da.b	4
		720.2.da.c	4
		720.2.da.d	4
		720.2.da.e	544
720.2.db	\(\chi_{720}(61, \cdot)\)	720.2.db.a	384	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(720))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(720)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 1}\)