Space of modular forms of level 1080 and weight 2

• Label: 1080.2
• Level: 1080
• Weight: 2
• Dimension: 12480
• Nonzero newspaces: 27
• Sturm bound: 124416
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 27 \)
Sturm bound:			\(124416\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1080))\).

	Total	New	Old
Modular forms	32544	12864	19680
Cusp forms	29665	12480	17185
Eisenstein series	2879	384	2495

Trace form

12480 * q - 16 * q^2 - 24 * q^3 - 28 * q^4 + 2 * q^5 - 72 * q^6 - 28 * q^7 - 28 * q^8 - 48 * q^9 - 50 * q^10 - 72 * q^11 - 24 * q^12 - 20 * q^13 - 28 * q^14 - 48 * q^15 - 92 * q^16 - 84 * q^17 - 24 * q^18 - 60 * q^19 - 18 * q^20 - 24 * q^21 + 12 * q^22 - 84 * q^23 + 12 * q^24 - 106 * q^25 + 36 * q^26 + 6 * q^27 + 24 * q^28 + 36 * q^29 + 12 * q^30 - 60 * q^31 + 204 * q^32 - 30 * q^33 + 68 * q^34 + 34 * q^35 + 48 * q^36 + 44 * q^37 + 220 * q^38 + 48 * q^39 + 18 * q^40 - 60 * q^41 + 96 * q^42 + 44 * q^43 + 204 * q^44 + 54 * q^45 + 4 * q^46 + 160 * q^47 + 12 * q^48 - 98 * q^49 + 66 * q^50 + 48 * q^51 + 76 * q^52 + 64 * q^53 - 24 * q^54 - 22 * q^55 - 92 * q^56 + 42 * q^57 - 12 * q^58 + 238 * q^59 - 96 * q^60 + 28 * q^61 - 156 * q^62 + 168 * q^63 - 52 * q^64 + 66 * q^65 - 252 * q^66 + 132 * q^67 - 228 * q^68 + 96 * q^69 - 86 * q^70 + 244 * q^71 - 192 * q^72 + 28 * q^73 - 284 * q^74 + 102 * q^75 - 316 * q^76 + 208 * q^77 - 252 * q^78 + 148 * q^79 - 166 * q^80 - 24 * q^81 - 144 * q^82 + 308 * q^83 - 156 * q^84 + 84 * q^85 - 276 * q^86 + 108 * q^87 - 36 * q^88 + 126 * q^89 - 174 * q^90 + 88 * q^91 - 172 * q^92 + 28 * q^94 + 168 * q^95 - 384 * q^96 + 52 * q^97 - 316 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1080))\)

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
1080.2.a	\(\chi_{1080}(1, \cdot)\)	1080.2.a.a	1	1
		1080.2.a.b	1
		1080.2.a.c	1
		1080.2.a.d	1
		1080.2.a.e	1
		1080.2.a.f	1
		1080.2.a.g	1
		1080.2.a.h	1
		1080.2.a.i	1
		1080.2.a.j	1
		1080.2.a.k	1
		1080.2.a.l	1
		1080.2.a.m	2
		1080.2.a.n	2
1080.2.b	\(\chi_{1080}(971, \cdot)\)	1080.2.b.a	16	1
		1080.2.b.b	16
		1080.2.b.c	16
		1080.2.b.d	16
1080.2.d	\(\chi_{1080}(109, \cdot)\)	1080.2.d.a	4	1
		1080.2.d.b	4
		1080.2.d.c	4
		1080.2.d.d	4
		1080.2.d.e	4
		1080.2.d.f	4
		1080.2.d.g	16
		1080.2.d.h	16
		1080.2.d.i	20
		1080.2.d.j	20
1080.2.f	\(\chi_{1080}(649, \cdot)\)	1080.2.f.a	2	1
		1080.2.f.b	2
		1080.2.f.c	2
		1080.2.f.d	2
		1080.2.f.e	4
		1080.2.f.f	4
		1080.2.f.g	8
1080.2.h	\(\chi_{1080}(431, \cdot)\)	None	0	1
1080.2.k	\(\chi_{1080}(541, \cdot)\)	1080.2.k.a	12	1
		1080.2.k.b	16
		1080.2.k.c	16
		1080.2.k.d	20
1080.2.m	\(\chi_{1080}(539, \cdot)\)	1080.2.m.a	8	1
		1080.2.m.b	40
		1080.2.m.c	48
1080.2.o	\(\chi_{1080}(1079, \cdot)\)	None	0	1
1080.2.q	\(\chi_{1080}(361, \cdot)\)	1080.2.q.a	2	2
		1080.2.q.b	4
		1080.2.q.c	4
		1080.2.q.d	6
		1080.2.q.e	8
1080.2.s	\(\chi_{1080}(377, \cdot)\)	1080.2.s.a	24	2
		1080.2.s.b	24
1080.2.t	\(\chi_{1080}(487, \cdot)\)	None	0	2
1080.2.w	\(\chi_{1080}(163, \cdot)\)	n/a	192	2
1080.2.x	\(\chi_{1080}(53, \cdot)\)	n/a	192	2
1080.2.bb	\(\chi_{1080}(359, \cdot)\)	None	0	2
1080.2.bd	\(\chi_{1080}(179, \cdot)\)	n/a	136	2
1080.2.bf	\(\chi_{1080}(181, \cdot)\)	1080.2.bf.a	4	2
		1080.2.bf.b	92
1080.2.bg	\(\chi_{1080}(71, \cdot)\)	None	0	2
1080.2.bi	\(\chi_{1080}(289, \cdot)\)	1080.2.bi.a	4	2
		1080.2.bi.b	32
1080.2.bk	\(\chi_{1080}(469, \cdot)\)	n/a	136	2
1080.2.bm	\(\chi_{1080}(251, \cdot)\)	1080.2.bm.a	48	2
		1080.2.bm.b	48
1080.2.bo	\(\chi_{1080}(121, \cdot)\)	n/a	216	6
1080.2.bp	\(\chi_{1080}(307, \cdot)\)	n/a	272	4
1080.2.bs	\(\chi_{1080}(197, \cdot)\)	n/a	272	4
1080.2.bt	\(\chi_{1080}(17, \cdot)\)	1080.2.bt.a	72	4
1080.2.bw	\(\chi_{1080}(127, \cdot)\)	None	0	4
1080.2.bx	\(\chi_{1080}(59, \cdot)\)	n/a	1272	6
1080.2.cc	\(\chi_{1080}(61, \cdot)\)	n/a	864	6
1080.2.cd	\(\chi_{1080}(119, \cdot)\)	None	0	6
1080.2.cg	\(\chi_{1080}(49, \cdot)\)	n/a	324	6
1080.2.ch	\(\chi_{1080}(11, \cdot)\)	n/a	864	6
1080.2.ci	\(\chi_{1080}(191, \cdot)\)	None	0	6
1080.2.cj	\(\chi_{1080}(229, \cdot)\)	n/a	1272	6
1080.2.co	\(\chi_{1080}(77, \cdot)\)	n/a	2544	12
1080.2.cp	\(\chi_{1080}(7, \cdot)\)	None	0	12
1080.2.cs	\(\chi_{1080}(113, \cdot)\)	n/a	648	12
1080.2.ct	\(\chi_{1080}(43, \cdot)\)	n/a	2544	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1080)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1080))\)\(^{\oplus 1}\)