Space of modular forms of level 1584 and weight 4

• Label: 1584.4
• Level: 1584
• Weight: 4
• Dimension: 90437
• Nonzero newspaces: 32
• Sturm bound: 552960
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(552960\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1584))\).

	Total	New	Old
Modular forms	209600	91165	118435
Cusp forms	205120	90437	114683
Eisenstein series	4480	728	3752

Trace form

90437 * q - 48 * q^2 - 48 * q^3 - 68 * q^4 - 61 * q^5 - 64 * q^6 - 63 * q^7 + 36 * q^8 + 24 * q^9 - 12 * q^10 + 30 * q^11 - 144 * q^12 + 39 * q^13 - 300 * q^14 - 6 * q^15 + 444 * q^16 + 97 * q^17 + 216 * q^18 - 379 * q^19 - 892 * q^20 - 678 * q^21 - 476 * q^22 - 728 * q^23 - 1536 * q^24 - 1365 * q^25 - 1700 * q^26 + 708 * q^27 - 996 * q^28 + 499 * q^29 + 936 * q^30 - 267 * q^31 + 1932 * q^32 - 117 * q^33 + 1800 * q^34 + 201 * q^35 - 1592 * q^36 + 1715 * q^37 - 2404 * q^38 + 402 * q^39 + 1468 * q^40 + 1699 * q^41 + 1296 * q^42 - 1704 * q^43 + 2156 * q^44 + 346 * q^45 + 3476 * q^46 - 6741 * q^47 + 4824 * q^48 - 2569 * q^49 + 7152 * q^50 - 3968 * q^51 + 3876 * q^52 + 237 * q^53 + 376 * q^54 - 799 * q^55 - 5880 * q^56 - 2316 * q^57 - 4580 * q^58 + 8645 * q^59 - 15928 * q^60 + 2247 * q^61 - 9516 * q^62 + 5034 * q^63 - 3332 * q^64 + 3678 * q^65 + 4848 * q^66 - 5776 * q^67 + 6820 * q^68 + 5626 * q^69 - 136 * q^70 - 1763 * q^71 + 15840 * q^72 - 1929 * q^73 + 17632 * q^74 + 1000 * q^75 + 4708 * q^76 + 7088 * q^77 + 888 * q^78 + 1523 * q^79 - 20256 * q^80 + 808 * q^81 - 18444 * q^82 - 353 * q^83 - 19168 * q^84 - 2375 * q^85 - 31260 * q^86 + 438 * q^87 - 23088 * q^88 - 8438 * q^89 - 2368 * q^90 + 6105 * q^91 + 14220 * q^92 - 1822 * q^93 + 13372 * q^94 + 1149 * q^95 + 12856 * q^96 - 4865 * q^97 + 33948 * q^98 + 1515 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1584))\)

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
1584.4.a	\(\chi_{1584}(1, \cdot)\)	1584.4.a.a	1	1
		1584.4.a.b	1
		1584.4.a.c	1
		1584.4.a.d	1
		1584.4.a.e	1
		1584.4.a.f	1
		1584.4.a.g	1
		1584.4.a.h	1
		1584.4.a.i	1
		1584.4.a.j	1
		1584.4.a.k	1
		1584.4.a.l	1
		1584.4.a.m	1
		1584.4.a.n	1
		1584.4.a.o	1
		1584.4.a.p	1
		1584.4.a.q	1
		1584.4.a.r	1
		1584.4.a.s	1
		1584.4.a.t	1
		1584.4.a.u	1
		1584.4.a.v	1
		1584.4.a.w	2
		1584.4.a.x	2
		1584.4.a.y	2
		1584.4.a.z	2
		1584.4.a.ba	2
		1584.4.a.bb	2
		1584.4.a.bc	2
		1584.4.a.bd	2
		1584.4.a.be	2
		1584.4.a.bf	2
		1584.4.a.bg	2
		1584.4.a.bh	2
		1584.4.a.bi	2
		1584.4.a.bj	2
		1584.4.a.bk	2
		1584.4.a.bl	3
		1584.4.a.bm	3
		1584.4.a.bn	3
		1584.4.a.bo	3
		1584.4.a.bp	3
		1584.4.a.bq	4
		1584.4.a.br	4
1584.4.b	\(\chi_{1584}(593, \cdot)\)	1584.4.b.a	2	1
		1584.4.b.b	2
		1584.4.b.c	6
		1584.4.b.d	6
		1584.4.b.e	6
		1584.4.b.f	6
		1584.4.b.g	8
		1584.4.b.h	18
		1584.4.b.i	18
1584.4.d	\(\chi_{1584}(287, \cdot)\)	1584.4.d.a	10	1
		1584.4.d.b	10
		1584.4.d.c	20
		1584.4.d.d	20
1584.4.f	\(\chi_{1584}(793, \cdot)\)	None	0	1
1584.4.h	\(\chi_{1584}(1495, \cdot)\)	None	0	1
1584.4.k	\(\chi_{1584}(1079, \cdot)\)	None	0	1
1584.4.m	\(\chi_{1584}(1385, \cdot)\)	None	0	1
1584.4.o	\(\chi_{1584}(703, \cdot)\)	1584.4.o.a	2	1
		1584.4.o.b	2
		1584.4.o.c	2
		1584.4.o.d	4
		1584.4.o.e	4
		1584.4.o.f	8
		1584.4.o.g	8
		1584.4.o.h	12
		1584.4.o.i	24
		1584.4.o.j	24
1584.4.q	\(\chi_{1584}(529, \cdot)\)	n/a	360	2
1584.4.r	\(\chi_{1584}(307, \cdot)\)	n/a	716	2
1584.4.u	\(\chi_{1584}(397, \cdot)\)	n/a	600	2
1584.4.v	\(\chi_{1584}(683, \cdot)\)	n/a	480	2
1584.4.y	\(\chi_{1584}(197, \cdot)\)	n/a	576	2
1584.4.z	\(\chi_{1584}(289, \cdot)\)	n/a	356	4
1584.4.bc	\(\chi_{1584}(175, \cdot)\)	n/a	432	2
1584.4.be	\(\chi_{1584}(329, \cdot)\)	None	0	2
1584.4.bg	\(\chi_{1584}(23, \cdot)\)	None	0	2
1584.4.bh	\(\chi_{1584}(439, \cdot)\)	None	0	2
1584.4.bj	\(\chi_{1584}(265, \cdot)\)	None	0	2
1584.4.bl	\(\chi_{1584}(815, \cdot)\)	n/a	360	2
1584.4.bn	\(\chi_{1584}(65, \cdot)\)	n/a	428	2
1584.4.bq	\(\chi_{1584}(127, \cdot)\)	n/a	360	4
1584.4.bs	\(\chi_{1584}(233, \cdot)\)	None	0	4
1584.4.bu	\(\chi_{1584}(71, \cdot)\)	None	0	4
1584.4.bx	\(\chi_{1584}(343, \cdot)\)	None	0	4
1584.4.bz	\(\chi_{1584}(361, \cdot)\)	None	0	4
1584.4.cb	\(\chi_{1584}(575, \cdot)\)	n/a	288	4
1584.4.cd	\(\chi_{1584}(17, \cdot)\)	n/a	288	4
1584.4.cf	\(\chi_{1584}(155, \cdot)\)	n/a	2880	4
1584.4.cg	\(\chi_{1584}(461, \cdot)\)	n/a	3440	4
1584.4.cj	\(\chi_{1584}(43, \cdot)\)	n/a	3440	4
1584.4.ck	\(\chi_{1584}(133, \cdot)\)	n/a	2880	4
1584.4.cm	\(\chi_{1584}(49, \cdot)\)	n/a	1712	8
1584.4.cn	\(\chi_{1584}(413, \cdot)\)	n/a	2304	8
1584.4.cq	\(\chi_{1584}(179, \cdot)\)	n/a	2304	8
1584.4.cr	\(\chi_{1584}(37, \cdot)\)	n/a	2864	8
1584.4.cu	\(\chi_{1584}(19, \cdot)\)	n/a	2864	8
1584.4.cw	\(\chi_{1584}(497, \cdot)\)	n/a	1712	8
1584.4.cy	\(\chi_{1584}(47, \cdot)\)	n/a	1728	8
1584.4.da	\(\chi_{1584}(25, \cdot)\)	None	0	8
1584.4.dc	\(\chi_{1584}(7, \cdot)\)	None	0	8
1584.4.dd	\(\chi_{1584}(119, \cdot)\)	None	0	8
1584.4.df	\(\chi_{1584}(41, \cdot)\)	None	0	8
1584.4.dh	\(\chi_{1584}(79, \cdot)\)	n/a	1728	8
1584.4.dl	\(\chi_{1584}(157, \cdot)\)	n/a	13760	16
1584.4.dm	\(\chi_{1584}(139, \cdot)\)	n/a	13760	16
1584.4.dp	\(\chi_{1584}(29, \cdot)\)	n/a	13760	16
1584.4.dq	\(\chi_{1584}(59, \cdot)\)	n/a	13760	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1584))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1584)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)