Space of modular forms of level 1584 and weight 2

• Label: 1584.2
• Level: 1584
• Weight: 2
• Dimension: 29903
• Nonzero newspaces: 32
• Sturm bound: 276480
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(276480\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1584))\).

	Total	New	Old
Modular forms	71360	30631	40729
Cusp forms	66881	29903	36978
Eisenstein series	4479	728	3751

Trace form

29903 * q - 48 * q^2 - 48 * q^3 - 52 * q^4 - 65 * q^5 - 64 * q^6 - 47 * q^7 - 60 * q^8 - 24 * q^9 - 148 * q^10 - 54 * q^11 - 144 * q^12 - 77 * q^13 - 12 * q^14 - 54 * q^15 - 4 * q^16 - 91 * q^17 - 24 * q^18 - 115 * q^19 + 52 * q^20 - 54 * q^21 - 8 * q^22 - 40 * q^23 + 41 * q^25 + 68 * q^26 - 12 * q^27 - 68 * q^28 - q^29 - 24 * q^30 - 11 * q^31 + 12 * q^32 - 141 * q^33 - 88 * q^34 + 81 * q^35 - 56 * q^36 - 217 * q^37 - 140 * q^38 + 66 * q^39 - 164 * q^40 - 25 * q^41 - 144 * q^42 + 56 * q^43 - 140 * q^44 - 134 * q^45 - 268 * q^46 + 75 * q^47 - 168 * q^48 - 215 * q^49 - 216 * q^50 + 16 * q^51 - 172 * q^52 - 63 * q^53 - 152 * q^54 - 87 * q^55 - 312 * q^56 - 60 * q^57 - 124 * q^58 + 13 * q^59 - 280 * q^60 - 13 * q^61 - 252 * q^62 - 54 * q^63 - 4 * q^64 - 282 * q^65 - 192 * q^66 - 104 * q^67 - 220 * q^68 - 230 * q^69 + 168 * q^70 - 163 * q^71 - 288 * q^72 + 75 * q^73 - 64 * q^74 - 152 * q^75 + 180 * q^76 - 32 * q^77 - 360 * q^78 - 77 * q^79 - 96 * q^80 - 296 * q^81 + 36 * q^82 - 193 * q^83 - 352 * q^84 + 161 * q^85 - 180 * q^86 - 186 * q^87 + 192 * q^88 + 14 * q^89 - 352 * q^90 - 215 * q^91 - 84 * q^92 + 2 * q^93 - 4 * q^94 - 195 * q^95 - 200 * q^96 + 35 * q^97 - 12 * q^98 - 69 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1584))\)

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
1584.2.a	\(\chi_{1584}(1, \cdot)\)	1584.2.a.a	1	1
		1584.2.a.b	1
		1584.2.a.c	1
		1584.2.a.d	1
		1584.2.a.e	1
		1584.2.a.f	1
		1584.2.a.g	1
		1584.2.a.h	1
		1584.2.a.i	1
		1584.2.a.j	1
		1584.2.a.k	1
		1584.2.a.l	1
		1584.2.a.m	1
		1584.2.a.n	1
		1584.2.a.o	1
		1584.2.a.p	1
		1584.2.a.q	1
		1584.2.a.r	1
		1584.2.a.s	1
		1584.2.a.t	2
		1584.2.a.u	2
		1584.2.a.v	2
1584.2.b	\(\chi_{1584}(593, \cdot)\)	1584.2.b.a	2	1
		1584.2.b.b	2
		1584.2.b.c	2
		1584.2.b.d	2
		1584.2.b.e	4
		1584.2.b.f	6
		1584.2.b.g	6
1584.2.d	\(\chi_{1584}(287, \cdot)\)	1584.2.d.a	2	1
		1584.2.d.b	2
		1584.2.d.c	8
		1584.2.d.d	8
1584.2.f	\(\chi_{1584}(793, \cdot)\)	None	0	1
1584.2.h	\(\chi_{1584}(1495, \cdot)\)	None	0	1
1584.2.k	\(\chi_{1584}(1079, \cdot)\)	None	0	1
1584.2.m	\(\chi_{1584}(1385, \cdot)\)	None	0	1
1584.2.o	\(\chi_{1584}(703, \cdot)\)	1584.2.o.a	2	1
		1584.2.o.b	4
		1584.2.o.c	4
		1584.2.o.d	4
		1584.2.o.e	4
		1584.2.o.f	4
		1584.2.o.g	8
1584.2.q	\(\chi_{1584}(529, \cdot)\)	n/a	120	2
1584.2.r	\(\chi_{1584}(307, \cdot)\)	n/a	236	2
1584.2.u	\(\chi_{1584}(397, \cdot)\)	n/a	200	2
1584.2.v	\(\chi_{1584}(683, \cdot)\)	n/a	160	2
1584.2.y	\(\chi_{1584}(197, \cdot)\)	n/a	192	2
1584.2.z	\(\chi_{1584}(289, \cdot)\)	n/a	116	4
1584.2.bc	\(\chi_{1584}(175, \cdot)\)	n/a	144	2
1584.2.be	\(\chi_{1584}(329, \cdot)\)	None	0	2
1584.2.bg	\(\chi_{1584}(23, \cdot)\)	None	0	2
1584.2.bh	\(\chi_{1584}(439, \cdot)\)	None	0	2
1584.2.bj	\(\chi_{1584}(265, \cdot)\)	None	0	2
1584.2.bl	\(\chi_{1584}(815, \cdot)\)	n/a	120	2
1584.2.bn	\(\chi_{1584}(65, \cdot)\)	n/a	140	2
1584.2.bq	\(\chi_{1584}(127, \cdot)\)	n/a	120	4
1584.2.bs	\(\chi_{1584}(233, \cdot)\)	None	0	4
1584.2.bu	\(\chi_{1584}(71, \cdot)\)	None	0	4
1584.2.bx	\(\chi_{1584}(343, \cdot)\)	None	0	4
1584.2.bz	\(\chi_{1584}(361, \cdot)\)	None	0	4
1584.2.cb	\(\chi_{1584}(575, \cdot)\)	1584.2.cb.a	32	4
		1584.2.cb.b	64
1584.2.cd	\(\chi_{1584}(17, \cdot)\)	1584.2.cd.a	8	4
		1584.2.cd.b	8
		1584.2.cd.c	16
		1584.2.cd.d	16
		1584.2.cd.e	24
		1584.2.cd.f	24
1584.2.cf	\(\chi_{1584}(155, \cdot)\)	n/a	960	4
1584.2.cg	\(\chi_{1584}(461, \cdot)\)	n/a	1136	4
1584.2.cj	\(\chi_{1584}(43, \cdot)\)	n/a	1136	4
1584.2.ck	\(\chi_{1584}(133, \cdot)\)	n/a	960	4
1584.2.cm	\(\chi_{1584}(49, \cdot)\)	n/a	560	8
1584.2.cn	\(\chi_{1584}(413, \cdot)\)	n/a	768	8
1584.2.cq	\(\chi_{1584}(179, \cdot)\)	n/a	768	8
1584.2.cr	\(\chi_{1584}(37, \cdot)\)	n/a	944	8
1584.2.cu	\(\chi_{1584}(19, \cdot)\)	n/a	944	8
1584.2.cw	\(\chi_{1584}(497, \cdot)\)	n/a	560	8
1584.2.cy	\(\chi_{1584}(47, \cdot)\)	n/a	576	8
1584.2.da	\(\chi_{1584}(25, \cdot)\)	None	0	8
1584.2.dc	\(\chi_{1584}(7, \cdot)\)	None	0	8
1584.2.dd	\(\chi_{1584}(119, \cdot)\)	None	0	8
1584.2.df	\(\chi_{1584}(41, \cdot)\)	None	0	8
1584.2.dh	\(\chi_{1584}(79, \cdot)\)	n/a	576	8
1584.2.dl	\(\chi_{1584}(157, \cdot)\)	n/a	4544	16
1584.2.dm	\(\chi_{1584}(139, \cdot)\)	n/a	4544	16
1584.2.dp	\(\chi_{1584}(29, \cdot)\)	n/a	4544	16
1584.2.dq	\(\chi_{1584}(59, \cdot)\)	n/a	4544	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1584))\) into lower level spaces

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