Space of modular forms of level 1440 and weight 3

• Label: 1440.3
• Level: 1440
• Weight: 3
• Dimension: 44874
• Nonzero newspaces: 40
• Sturm bound: 331776
• Trace bound: 53

Defining parameters

Level:	\( N \)	=	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(331776\)
Trace bound:			\(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1440))\).

	Total	New	Old
Modular forms	112640	45414	67226
Cusp forms	108544	44874	63670
Eisenstein series	4096	540	3556

Trace form

44874 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 40 * q^5 - 96 * q^6 - 16 * q^7 - 24 * q^8 - 48 * q^9 - 68 * q^10 - 16 * q^11 - 32 * q^12 + 32 * q^13 + 8 * q^14 - 18 * q^15 - 112 * q^16 + 100 * q^17 - 32 * q^18 + 12 * q^19 - 116 * q^20 - 32 * q^21 - 320 * q^22 + 104 * q^23 - 32 * q^24 - 78 * q^25 - 272 * q^26 - 120 * q^27 - 192 * q^28 - 272 * q^29 - 80 * q^30 - 188 * q^31 + 16 * q^32 - 312 * q^33 + 64 * q^34 - 228 * q^35 - 624 * q^36 - 512 * q^37 - 1256 * q^38 - 252 * q^39 - 528 * q^40 - 796 * q^41 - 832 * q^42 - 564 * q^43 - 712 * q^44 - 144 * q^45 - 408 * q^46 - 240 * q^47 + 176 * q^48 - 118 * q^49 + 276 * q^50 + 16 * q^51 + 408 * q^52 + 1072 * q^53 + 1200 * q^54 - 80 * q^55 + 1696 * q^56 + 144 * q^57 + 1728 * q^58 - 152 * q^59 + 680 * q^60 + 944 * q^61 + 1104 * q^62 - 468 * q^63 - 336 * q^64 - 476 * q^65 - 96 * q^66 + 268 * q^67 - 16 * q^68 - 288 * q^69 - 672 * q^70 + 208 * q^71 - 32 * q^72 - 668 * q^73 + 152 * q^74 + 206 * q^75 + 568 * q^76 - 152 * q^77 + 784 * q^78 - 1820 * q^79 + 1728 * q^80 + 784 * q^81 + 3288 * q^82 - 2892 * q^83 + 2432 * q^84 + 144 * q^85 + 3184 * q^86 - 1532 * q^87 + 2448 * q^88 - 52 * q^89 + 672 * q^90 - 1704 * q^91 + 2432 * q^92 - 32 * q^93 + 1824 * q^94 + 216 * q^95 - 368 * q^96 + 1012 * q^97 + 32 * q^98 + 932 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1440))\)

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
1440.3.c	\(\chi_{1440}(449, \cdot)\)	1440.3.c.a	4	1
		1440.3.c.b	4
		1440.3.c.c	16
		1440.3.c.d	24
1440.3.e	\(\chi_{1440}(991, \cdot)\)	1440.3.e.a	4	1
		1440.3.e.b	4
		1440.3.e.c	8
		1440.3.e.d	8
		1440.3.e.e	8
		1440.3.e.f	8
1440.3.g	\(\chi_{1440}(271, \cdot)\)	1440.3.g.a	8	1
		1440.3.g.b	16
		1440.3.g.c	16
1440.3.i	\(\chi_{1440}(1169, \cdot)\)	1440.3.i.a	48	1
1440.3.j	\(\chi_{1440}(1279, \cdot)\)	1440.3.j.a	6	1
		1440.3.j.b	6
		1440.3.j.c	12
		1440.3.j.d	12
		1440.3.j.e	12
		1440.3.j.f	12
1440.3.l	\(\chi_{1440}(161, \cdot)\)	1440.3.l.a	8	1
		1440.3.l.b	8
		1440.3.l.c	8
		1440.3.l.d	8
1440.3.n	\(\chi_{1440}(881, \cdot)\)	1440.3.n.a	32	1
1440.3.p	\(\chi_{1440}(559, \cdot)\)	1440.3.p.a	1	1
		1440.3.p.b	1
		1440.3.p.c	2
		1440.3.p.d	2
		1440.3.p.e	2
		1440.3.p.f	2
		1440.3.p.g	8
		1440.3.p.h	16
		1440.3.p.i	24
1440.3.r	\(\chi_{1440}(199, \cdot)\)	None	0	2
1440.3.s	\(\chi_{1440}(521, \cdot)\)	None	0	2
1440.3.v	\(\chi_{1440}(143, \cdot)\)	1440.3.v.a	96	2
1440.3.y	\(\chi_{1440}(433, \cdot)\)	n/a	116	2
1440.3.ba	\(\chi_{1440}(503, \cdot)\)	None	0	2
1440.3.bb	\(\chi_{1440}(73, \cdot)\)	None	0	2
1440.3.be	\(\chi_{1440}(1223, \cdot)\)	None	0	2
1440.3.bf	\(\chi_{1440}(793, \cdot)\)	None	0	2
1440.3.bh	\(\chi_{1440}(577, \cdot)\)	n/a	120	2
1440.3.bk	\(\chi_{1440}(287, \cdot)\)	1440.3.bk.a	4	2
		1440.3.bk.b	4
		1440.3.bk.c	4
		1440.3.bk.d	4
		1440.3.bk.e	20
		1440.3.bk.f	20
		1440.3.bk.g	20
		1440.3.bk.h	20
1440.3.bn	\(\chi_{1440}(89, \cdot)\)	None	0	2
1440.3.bo	\(\chi_{1440}(631, \cdot)\)	None	0	2
1440.3.bp	\(\chi_{1440}(79, \cdot)\)	n/a	280	2
1440.3.bq	\(\chi_{1440}(401, \cdot)\)	n/a	192	2
1440.3.bs	\(\chi_{1440}(641, \cdot)\)	n/a	192	2
1440.3.bu	\(\chi_{1440}(319, \cdot)\)	n/a	288	2
1440.3.bx	\(\chi_{1440}(209, \cdot)\)	n/a	280	2
1440.3.bz	\(\chi_{1440}(751, \cdot)\)	n/a	192	2
1440.3.cb	\(\chi_{1440}(31, \cdot)\)	n/a	192	2
1440.3.cd	\(\chi_{1440}(929, \cdot)\)	n/a	288	2
1440.3.cf	\(\chi_{1440}(37, \cdot)\)	n/a	952	4
1440.3.cg	\(\chi_{1440}(467, \cdot)\)	n/a	768	4
1440.3.cj	\(\chi_{1440}(91, \cdot)\)	n/a	640	4
1440.3.ck	\(\chi_{1440}(269, \cdot)\)	n/a	768	4
1440.3.cm	\(\chi_{1440}(19, \cdot)\)	n/a	952	4
1440.3.cp	\(\chi_{1440}(341, \cdot)\)	n/a	512	4
1440.3.cq	\(\chi_{1440}(107, \cdot)\)	n/a	768	4
1440.3.ct	\(\chi_{1440}(397, \cdot)\)	n/a	952	4
1440.3.cw	\(\chi_{1440}(151, \cdot)\)	None	0	4
1440.3.cx	\(\chi_{1440}(329, \cdot)\)	None	0	4
1440.3.cz	\(\chi_{1440}(97, \cdot)\)	n/a	576	4
1440.3.da	\(\chi_{1440}(383, \cdot)\)	n/a	576	4
1440.3.dd	\(\chi_{1440}(313, \cdot)\)	None	0	4
1440.3.de	\(\chi_{1440}(263, \cdot)\)	None	0	4
1440.3.dh	\(\chi_{1440}(553, \cdot)\)	None	0	4
1440.3.di	\(\chi_{1440}(23, \cdot)\)	None	0	4
1440.3.dl	\(\chi_{1440}(47, \cdot)\)	n/a	560	4
1440.3.dm	\(\chi_{1440}(337, \cdot)\)	n/a	560	4
1440.3.do	\(\chi_{1440}(41, \cdot)\)	None	0	4
1440.3.dp	\(\chi_{1440}(439, \cdot)\)	None	0	4
1440.3.ds	\(\chi_{1440}(133, \cdot)\)	n/a	4576	8
1440.3.dv	\(\chi_{1440}(83, \cdot)\)	n/a	4576	8
1440.3.dx	\(\chi_{1440}(29, \cdot)\)	n/a	4576	8
1440.3.dy	\(\chi_{1440}(211, \cdot)\)	n/a	3072	8
1440.3.ea	\(\chi_{1440}(101, \cdot)\)	n/a	3072	8
1440.3.ed	\(\chi_{1440}(139, \cdot)\)	n/a	4576	8
1440.3.ef	\(\chi_{1440}(203, \cdot)\)	n/a	4576	8
1440.3.eg	\(\chi_{1440}(13, \cdot)\)	n/a	4576	8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1440))\) into lower level spaces

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