Space of modular forms of level 1440 and weight 5

• Label: 1440.5
• Level: 1440
• Weight: 5
• Dimension: 90018
• Nonzero newspaces: 40
• Sturm bound: 552960
• Trace bound: 53

Defining parameters

Level:	\( N \)	=	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(552960\)
Trace bound:			\(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(1440))\).

	Total	New	Old
Modular forms	223232	90558	132674
Cusp forms	219136	90018	129118
Eisenstein series	4096	540	3556

Trace form

90018 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 12 * q^5 - 96 * q^6 - 16 * q^7 - 24 * q^8 - 48 * q^9 + 92 * q^10 - 240 * q^11 - 32 * q^12 - 488 * q^13 - 888 * q^14 + 126 * q^15 + 1168 * q^16 + 1236 * q^17 - 32 * q^18 - 1460 * q^19 + 1164 * q^20 - 2528 * q^21 - 3808 * q^22 + 2280 * q^23 - 32 * q^24 + 1818 * q^25 + 5328 * q^26 + 3624 * q^27 + 5568 * q^28 + 7992 * q^29 - 176 * q^30 - 316 * q^31 - 2544 * q^32 - 6168 * q^33 - 7232 * q^34 - 1188 * q^35 - 25968 * q^36 - 15352 * q^37 - 15144 * q^38 + 2340 * q^39 + 20976 * q^40 + 27444 * q^41 + 47168 * q^42 + 1196 * q^43 + 70968 * q^44 + 8208 * q^45 + 17256 * q^46 + 5712 * q^47 - 19792 * q^48 - 11742 * q^49 - 53388 * q^50 - 14480 * q^51 - 84840 * q^52 - 64200 * q^53 - 72720 * q^54 - 80 * q^55 - 42336 * q^56 - 45744 * q^57 + 43296 * q^58 + 13032 * q^59 + 35624 * q^60 + 23656 * q^61 + 115344 * q^62 + 49260 * q^63 - 47184 * q^64 + 5148 * q^65 - 96 * q^66 - 34004 * q^67 - 11280 * q^68 + 34272 * q^69 + 26736 * q^70 - 20016 * q^71 - 32 * q^72 + 30260 * q^73 + 37464 * q^74 - 29890 * q^75 + 41528 * q^76 - 63768 * q^77 + 108496 * q^78 - 126492 * q^79 + 100800 * q^80 - 94640 * q^81 - 21672 * q^82 + 63348 * q^83 - 115840 * q^84 - 62840 * q^85 - 310704 * q^86 + 309028 * q^87 - 288624 * q^88 + 110268 * q^89 - 111648 * q^90 + 213336 * q^91 - 226560 * q^92 - 32 * q^93 + 59232 * q^94 + 21576 * q^95 + 51856 * q^96 - 5596 * q^97 + 284832 * q^98 - 259228 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(1440))\)

We only show spaces with odd 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
1440.5.c	\(\chi_{1440}(449, \cdot)\)	1440.5.c.a	4	1
		1440.5.c.b	4
		1440.5.c.c	40
		1440.5.c.d	48
1440.5.e	\(\chi_{1440}(991, \cdot)\)	1440.5.e.a	8	1
		1440.5.e.b	8
		1440.5.e.c	16
		1440.5.e.d	16
		1440.5.e.e	16
		1440.5.e.f	16
1440.5.g	\(\chi_{1440}(271, \cdot)\)	1440.5.g.a	16	1
		1440.5.g.b	32
		1440.5.g.c	32
1440.5.i	\(\chi_{1440}(1169, \cdot)\)	1440.5.i.a	96	1
1440.5.j	\(\chi_{1440}(1279, \cdot)\)	n/a	120	1
1440.5.l	\(\chi_{1440}(161, \cdot)\)	1440.5.l.a	8	1
		1440.5.l.b	8
		1440.5.l.c	16
		1440.5.l.d	16
		1440.5.l.e	16
1440.5.n	\(\chi_{1440}(881, \cdot)\)	1440.5.n.a	64	1
1440.5.p	\(\chi_{1440}(559, \cdot)\)	n/a	118	1
1440.5.r	\(\chi_{1440}(199, \cdot)\)	None	0	2
1440.5.s	\(\chi_{1440}(521, \cdot)\)	None	0	2
1440.5.v	\(\chi_{1440}(143, \cdot)\)	n/a	192	2
1440.5.y	\(\chi_{1440}(433, \cdot)\)	n/a	236	2
1440.5.ba	\(\chi_{1440}(503, \cdot)\)	None	0	2
1440.5.bb	\(\chi_{1440}(73, \cdot)\)	None	0	2
1440.5.be	\(\chi_{1440}(1223, \cdot)\)	None	0	2
1440.5.bf	\(\chi_{1440}(793, \cdot)\)	None	0	2
1440.5.bh	\(\chi_{1440}(577, \cdot)\)	n/a	240	2
1440.5.bk	\(\chi_{1440}(287, \cdot)\)	n/a	192	2
1440.5.bn	\(\chi_{1440}(89, \cdot)\)	None	0	2
1440.5.bo	\(\chi_{1440}(631, \cdot)\)	None	0	2
1440.5.bp	\(\chi_{1440}(79, \cdot)\)	n/a	568	2
1440.5.bq	\(\chi_{1440}(401, \cdot)\)	n/a	384	2
1440.5.bs	\(\chi_{1440}(641, \cdot)\)	n/a	384	2
1440.5.bu	\(\chi_{1440}(319, \cdot)\)	n/a	576	2
1440.5.bx	\(\chi_{1440}(209, \cdot)\)	n/a	568	2
1440.5.bz	\(\chi_{1440}(751, \cdot)\)	n/a	384	2
1440.5.cb	\(\chi_{1440}(31, \cdot)\)	n/a	384	2
1440.5.cd	\(\chi_{1440}(929, \cdot)\)	n/a	576	2
1440.5.cf	\(\chi_{1440}(37, \cdot)\)	n/a	1912	4
1440.5.cg	\(\chi_{1440}(467, \cdot)\)	n/a	1536	4
1440.5.cj	\(\chi_{1440}(91, \cdot)\)	n/a	1280	4
1440.5.ck	\(\chi_{1440}(269, \cdot)\)	n/a	1536	4
1440.5.cm	\(\chi_{1440}(19, \cdot)\)	n/a	1912	4
1440.5.cp	\(\chi_{1440}(341, \cdot)\)	n/a	1024	4
1440.5.cq	\(\chi_{1440}(107, \cdot)\)	n/a	1536	4
1440.5.ct	\(\chi_{1440}(397, \cdot)\)	n/a	1912	4
1440.5.cw	\(\chi_{1440}(151, \cdot)\)	None	0	4
1440.5.cx	\(\chi_{1440}(329, \cdot)\)	None	0	4
1440.5.cz	\(\chi_{1440}(97, \cdot)\)	n/a	1152	4
1440.5.da	\(\chi_{1440}(383, \cdot)\)	n/a	1152	4
1440.5.dd	\(\chi_{1440}(313, \cdot)\)	None	0	4
1440.5.de	\(\chi_{1440}(263, \cdot)\)	None	0	4
1440.5.dh	\(\chi_{1440}(553, \cdot)\)	None	0	4
1440.5.di	\(\chi_{1440}(23, \cdot)\)	None	0	4
1440.5.dl	\(\chi_{1440}(47, \cdot)\)	n/a	1136	4
1440.5.dm	\(\chi_{1440}(337, \cdot)\)	n/a	1136	4
1440.5.do	\(\chi_{1440}(41, \cdot)\)	None	0	4
1440.5.dp	\(\chi_{1440}(439, \cdot)\)	None	0	4
1440.5.ds	\(\chi_{1440}(133, \cdot)\)	n/a	9184	8
1440.5.dv	\(\chi_{1440}(83, \cdot)\)	n/a	9184	8
1440.5.dx	\(\chi_{1440}(29, \cdot)\)	n/a	9184	8
1440.5.dy	\(\chi_{1440}(211, \cdot)\)	n/a	6144	8
1440.5.ea	\(\chi_{1440}(101, \cdot)\)	n/a	6144	8
1440.5.ed	\(\chi_{1440}(139, \cdot)\)	n/a	9184	8
1440.5.ef	\(\chi_{1440}(203, \cdot)\)	n/a	9184	8
1440.5.eg	\(\chi_{1440}(13, \cdot)\)	n/a	9184	8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(1440))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(1440)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 20}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 15}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)