Space of modular forms of level 1080 and weight 4

• Label: 1080.4
• Level: 1080
• Weight: 4
• Dimension: 37824
• Nonzero newspaces: 27
• Sturm bound: 248832
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 27 \)
Sturm bound:			\(248832\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1080))\).

	Total	New	Old
Modular forms	94752	38208	56544
Cusp forms	91872	37824	54048
Eisenstein series	2880	384	2496

Trace form

37824 * q - 16 * q^2 - 24 * q^3 - 28 * q^4 - 10 * q^5 - 72 * q^6 - 76 * q^7 - 28 * q^8 - 48 * q^9 + 30 * q^10 - 120 * q^11 - 24 * q^12 - 12 * q^13 + 116 * q^14 + 96 * q^15 + 36 * q^16 + 420 * q^17 - 24 * q^18 + 20 * q^19 - 306 * q^20 + 120 * q^21 - 468 * q^22 - 84 * q^23 + 300 * q^24 + 138 * q^25 + 2676 * q^26 + 870 * q^27 + 1208 * q^28 + 684 * q^29 - 276 * q^30 - 780 * q^31 - 3636 * q^32 - 570 * q^33 - 2236 * q^34 - 2126 * q^35 - 4272 * q^36 - 2220 * q^37 - 4580 * q^38 - 1680 * q^39 - 558 * q^40 + 444 * q^41 + 816 * q^42 - 964 * q^43 + 4620 * q^44 + 1674 * q^45 + 4196 * q^46 + 4432 * q^47 + 4332 * q^48 + 2794 * q^49 + 786 * q^50 - 3696 * q^51 - 500 * q^52 - 1088 * q^53 - 24 * q^54 - 190 * q^55 - 8540 * q^56 - 498 * q^57 - 7852 * q^58 + 8494 * q^59 - 3696 * q^60 + 900 * q^61 - 5388 * q^62 + 2760 * q^63 - 820 * q^64 - 1482 * q^65 + 7308 * q^66 - 9676 * q^67 + 13116 * q^68 - 192 * q^69 + 8090 * q^70 - 21068 * q^71 + 11904 * q^72 + 772 * q^73 + 22180 * q^74 + 1542 * q^75 + 12708 * q^76 + 1264 * q^77 + 3852 * q^78 + 3908 * q^79 + 5594 * q^80 + 408 * q^81 + 4496 * q^82 + 12932 * q^83 - 11244 * q^84 + 12 * q^85 - 22596 * q^86 + 7164 * q^87 - 7332 * q^88 - 8406 * q^89 - 21126 * q^90 - 3448 * q^91 - 27244 * q^92 - 12960 * q^93 - 452 * q^94 - 13080 * q^95 - 7872 * q^96 - 2900 * q^97 - 7828 * q^98 + 7596 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1080))\)

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
1080.4.a	\(\chi_{1080}(1, \cdot)\)	1080.4.a.a	2	1
		1080.4.a.b	2
		1080.4.a.c	3
		1080.4.a.d	3
		1080.4.a.e	3
		1080.4.a.f	3
		1080.4.a.g	3
		1080.4.a.h	3
		1080.4.a.i	3
		1080.4.a.j	3
		1080.4.a.k	3
		1080.4.a.l	3
		1080.4.a.m	3
		1080.4.a.n	3
		1080.4.a.o	4
		1080.4.a.p	4
1080.4.b	\(\chi_{1080}(971, \cdot)\)	n/a	192	1
1080.4.d	\(\chi_{1080}(109, \cdot)\)	n/a	288	1
1080.4.f	\(\chi_{1080}(649, \cdot)\)	1080.4.f.a	16	1
		1080.4.f.b	18
		1080.4.f.c	18
		1080.4.f.d	20
1080.4.h	\(\chi_{1080}(431, \cdot)\)	None	0	1
1080.4.k	\(\chi_{1080}(541, \cdot)\)	n/a	192	1
1080.4.m	\(\chi_{1080}(539, \cdot)\)	n/a	288	1
1080.4.o	\(\chi_{1080}(1079, \cdot)\)	None	0	1
1080.4.q	\(\chi_{1080}(361, \cdot)\)	1080.4.q.a	2	2
		1080.4.q.b	16
		1080.4.q.c	16
		1080.4.q.d	18
		1080.4.q.e	20
1080.4.s	\(\chi_{1080}(377, \cdot)\)	n/a	144	2
1080.4.t	\(\chi_{1080}(487, \cdot)\)	None	0	2
1080.4.w	\(\chi_{1080}(163, \cdot)\)	n/a	576	2
1080.4.x	\(\chi_{1080}(53, \cdot)\)	n/a	576	2
1080.4.bb	\(\chi_{1080}(359, \cdot)\)	None	0	2
1080.4.bd	\(\chi_{1080}(179, \cdot)\)	n/a	424	2
1080.4.bf	\(\chi_{1080}(181, \cdot)\)	n/a	288	2
1080.4.bg	\(\chi_{1080}(71, \cdot)\)	None	0	2
1080.4.bi	\(\chi_{1080}(289, \cdot)\)	n/a	108	2
1080.4.bk	\(\chi_{1080}(469, \cdot)\)	n/a	424	2
1080.4.bm	\(\chi_{1080}(251, \cdot)\)	n/a	288	2
1080.4.bo	\(\chi_{1080}(121, \cdot)\)	n/a	648	6
1080.4.bp	\(\chi_{1080}(307, \cdot)\)	n/a	848	4
1080.4.bs	\(\chi_{1080}(197, \cdot)\)	n/a	848	4
1080.4.bt	\(\chi_{1080}(17, \cdot)\)	n/a	216	4
1080.4.bw	\(\chi_{1080}(127, \cdot)\)	None	0	4
1080.4.bx	\(\chi_{1080}(59, \cdot)\)	n/a	3864	6
1080.4.cc	\(\chi_{1080}(61, \cdot)\)	n/a	2592	6
1080.4.cd	\(\chi_{1080}(119, \cdot)\)	None	0	6
1080.4.cg	\(\chi_{1080}(49, \cdot)\)	n/a	972	6
1080.4.ch	\(\chi_{1080}(11, \cdot)\)	n/a	2592	6
1080.4.ci	\(\chi_{1080}(191, \cdot)\)	None	0	6
1080.4.cj	\(\chi_{1080}(229, \cdot)\)	n/a	3864	6
1080.4.co	\(\chi_{1080}(77, \cdot)\)	n/a	7728	12
1080.4.cp	\(\chi_{1080}(7, \cdot)\)	None	0	12
1080.4.cs	\(\chi_{1080}(113, \cdot)\)	n/a	1944	12
1080.4.ct	\(\chi_{1080}(43, \cdot)\)	n/a	7728	12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1080))\) into lower level spaces

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