Space of modular forms of level 3024 and weight 2

• Label: 3024.2
• Level: 3024
• Weight: 2
• Dimension: 105264
• Nonzero newspaces: 64
• Sturm bound: 995328
• Trace bound: 45

Defining parameters

Level:	\( N \)	=	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 64 \)
Sturm bound:			\(995328\)
Trace bound:			\(45\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3024))\).

	Total	New	Old
Modular forms	253872	106704	147168
Cusp forms	243793	105264	138529
Eisenstein series	10079	1440	8639

Trace form

105264 * q - 64 * q^2 - 72 * q^3 - 112 * q^4 - 78 * q^5 - 96 * q^6 - 103 * q^7 - 160 * q^8 - 24 * q^9 - 112 * q^10 - 38 * q^11 - 96 * q^12 - 132 * q^13 - 88 * q^14 - 180 * q^15 - 128 * q^16 - 162 * q^17 - 96 * q^18 - 88 * q^19 - 120 * q^20 - 150 * q^21 - 328 * q^22 - 70 * q^23 - 96 * q^24 - 70 * q^25 - 128 * q^26 - 108 * q^27 - 344 * q^28 - 310 * q^29 - 96 * q^30 - 136 * q^31 - 104 * q^32 - 264 * q^33 - 128 * q^34 - 145 * q^35 - 240 * q^36 - 212 * q^37 - 8 * q^38 - 144 * q^39 - 48 * q^40 - 108 * q^41 - 120 * q^42 - 334 * q^43 + 24 * q^44 - 168 * q^45 - 16 * q^46 - 190 * q^47 - 96 * q^48 - 307 * q^49 - 72 * q^50 - 54 * q^51 - 48 * q^52 - 72 * q^53 - 96 * q^54 - 228 * q^55 + 100 * q^56 - 30 * q^57 + 80 * q^58 - 14 * q^59 + 144 * q^60 - 4 * q^61 + 416 * q^62 - 60 * q^63 - 136 * q^64 + 200 * q^65 + 264 * q^66 - 4 * q^67 + 488 * q^68 + 72 * q^69 + 52 * q^70 + 46 * q^71 + 240 * q^72 + 52 * q^73 + 496 * q^74 + 12 * q^75 + 272 * q^76 - 33 * q^77 + 72 * q^78 - 52 * q^79 + 600 * q^80 - 24 * q^81 - 32 * q^82 + 44 * q^83 + 12 * q^84 - 354 * q^85 + 440 * q^86 - 36 * q^87 + 96 * q^88 + 6 * q^89 + 120 * q^90 - 129 * q^91 - 40 * q^92 + 24 * q^93 - 48 * q^94 + 166 * q^95 - 96 * q^96 - 348 * q^97 - 4 * q^98 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3024))\)

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
3024.2.a	\(\chi_{3024}(1, \cdot)\)	3024.2.a.a	1	1
		3024.2.a.b	1
		3024.2.a.c	1
		3024.2.a.d	1
		3024.2.a.e	1
		3024.2.a.f	1
		3024.2.a.g	1
		3024.2.a.h	1
		3024.2.a.i	1
		3024.2.a.j	1
		3024.2.a.k	1
		3024.2.a.l	1
		3024.2.a.m	1
		3024.2.a.n	1
		3024.2.a.o	1
		3024.2.a.p	1
		3024.2.a.q	1
		3024.2.a.r	1
		3024.2.a.s	1
		3024.2.a.t	1
		3024.2.a.u	1
		3024.2.a.v	1
		3024.2.a.w	1
		3024.2.a.x	1
		3024.2.a.y	1
		3024.2.a.z	1
		3024.2.a.ba	1
		3024.2.a.bb	1
		3024.2.a.bc	1
		3024.2.a.bd	1
		3024.2.a.be	2
		3024.2.a.bf	2
		3024.2.a.bg	2
		3024.2.a.bh	2
		3024.2.a.bi	2
		3024.2.a.bj	2
		3024.2.a.bk	2
		3024.2.a.bl	2
		3024.2.a.bm	2
3024.2.b	\(\chi_{3024}(1567, \cdot)\)	3024.2.b.a	2	1
		3024.2.b.b	2
		3024.2.b.c	2
		3024.2.b.d	2
		3024.2.b.e	2
		3024.2.b.f	2
		3024.2.b.g	2
		3024.2.b.h	2
		3024.2.b.i	2
		3024.2.b.j	2
		3024.2.b.k	2
		3024.2.b.l	2
		3024.2.b.m	2
		3024.2.b.n	2
		3024.2.b.o	2
		3024.2.b.p	2
		3024.2.b.q	4
		3024.2.b.r	4
		3024.2.b.s	4
		3024.2.b.t	4
		3024.2.b.u	8
		3024.2.b.v	8
3024.2.c	\(\chi_{3024}(1513, \cdot)\)	None	0	1
3024.2.h	\(\chi_{3024}(2591, \cdot)\)	3024.2.h.a	8	1
		3024.2.h.b	8
		3024.2.h.c	8
		3024.2.h.d	8
		3024.2.h.e	8
		3024.2.h.f	8
3024.2.i	\(\chi_{3024}(377, \cdot)\)	None	0	1
3024.2.j	\(\chi_{3024}(1079, \cdot)\)	None	0	1
3024.2.k	\(\chi_{3024}(1889, \cdot)\)	3024.2.k.a	2	1
		3024.2.k.b	2
		3024.2.k.c	2
		3024.2.k.d	2
		3024.2.k.e	4
		3024.2.k.f	4
		3024.2.k.g	4
		3024.2.k.h	4
		3024.2.k.i	4
		3024.2.k.j	4
		3024.2.k.k	16
		3024.2.k.l	16
3024.2.p	\(\chi_{3024}(55, \cdot)\)	None	0	1
3024.2.q	\(\chi_{3024}(2305, \cdot)\)	3024.2.q.a	2	2
		3024.2.q.b	2
		3024.2.q.c	2
		3024.2.q.d	2
		3024.2.q.e	2
		3024.2.q.f	2
		3024.2.q.g	6
		3024.2.q.h	6
		3024.2.q.i	10
		3024.2.q.j	14
		3024.2.q.k	22
		3024.2.q.l	22
3024.2.r	\(\chi_{3024}(1009, \cdot)\)	3024.2.r.a	2	2
		3024.2.r.b	2
		3024.2.r.c	2
		3024.2.r.d	2
		3024.2.r.e	4
		3024.2.r.f	4
		3024.2.r.g	6
		3024.2.r.h	6
		3024.2.r.i	6
		3024.2.r.j	6
		3024.2.r.k	6
		3024.2.r.l	8
		3024.2.r.m	8
		3024.2.r.n	10
3024.2.s	\(\chi_{3024}(865, \cdot)\)	n/a	128	2
3024.2.t	\(\chi_{3024}(289, \cdot)\)	3024.2.t.a	2	2
		3024.2.t.b	2
		3024.2.t.c	2
		3024.2.t.d	2
		3024.2.t.e	2
		3024.2.t.f	2
		3024.2.t.g	6
		3024.2.t.h	6
		3024.2.t.i	10
		3024.2.t.j	14
		3024.2.t.k	22
		3024.2.t.l	22
3024.2.v	\(\chi_{3024}(323, \cdot)\)	n/a	384	2
3024.2.x	\(\chi_{3024}(811, \cdot)\)	n/a	512	2
3024.2.z	\(\chi_{3024}(757, \cdot)\)	n/a	384	2
3024.2.bb	\(\chi_{3024}(1133, \cdot)\)	n/a	512	2
3024.2.be	\(\chi_{3024}(361, \cdot)\)	None	0	2
3024.2.bf	\(\chi_{3024}(1711, \cdot)\)	3024.2.bf.a	2	2
		3024.2.bf.b	2
		3024.2.bf.c	2
		3024.2.bf.d	2
		3024.2.bf.e	4
		3024.2.bf.f	4
		3024.2.bf.g	24
		3024.2.bf.h	24
		3024.2.bf.i	32
3024.2.bg	\(\chi_{3024}(89, \cdot)\)	None	0	2
3024.2.bh	\(\chi_{3024}(1871, \cdot)\)	3024.2.bh.a	2	2
		3024.2.bh.b	2
		3024.2.bh.c	30
		3024.2.bh.d	30
		3024.2.bh.e	32
3024.2.bm	\(\chi_{3024}(1063, \cdot)\)	None	0	2
3024.2.bn	\(\chi_{3024}(1207, \cdot)\)	None	0	2
3024.2.bs	\(\chi_{3024}(1783, \cdot)\)	None	0	2
3024.2.bt	\(\chi_{3024}(593, \cdot)\)	n/a	128	2
3024.2.bu	\(\chi_{3024}(1943, \cdot)\)	None	0	2
3024.2.bz	\(\chi_{3024}(71, \cdot)\)	None	0	2
3024.2.ca	\(\chi_{3024}(2033, \cdot)\)	3024.2.ca.a	2	2
		3024.2.ca.b	10
		3024.2.ca.c	16
		3024.2.ca.d	16
		3024.2.ca.e	48
3024.2.cb	\(\chi_{3024}(1367, \cdot)\)	None	0	2
3024.2.cc	\(\chi_{3024}(881, \cdot)\)	3024.2.cc.a	12	2
		3024.2.cc.b	16
		3024.2.cc.c	16
		3024.2.cc.d	48
3024.2.ch	\(\chi_{3024}(575, \cdot)\)	3024.2.ch.a	24	2
		3024.2.ch.b	24
		3024.2.ch.c	24
3024.2.ci	\(\chi_{3024}(521, \cdot)\)	None	0	2
3024.2.cj	\(\chi_{3024}(1439, \cdot)\)	3024.2.cj.a	2	2
		3024.2.cj.b	2
		3024.2.cj.c	30
		3024.2.cj.d	30
		3024.2.cj.e	32
3024.2.ck	\(\chi_{3024}(1385, \cdot)\)	None	0	2
3024.2.cp	\(\chi_{3024}(2105, \cdot)\)	None	0	2
3024.2.cq	\(\chi_{3024}(431, \cdot)\)	n/a	128	2
3024.2.cr	\(\chi_{3024}(2377, \cdot)\)	None	0	2
3024.2.cs	\(\chi_{3024}(271, \cdot)\)	n/a	128	2
3024.2.cx	\(\chi_{3024}(559, \cdot)\)	3024.2.cx.a	2	2
		3024.2.cx.b	2
		3024.2.cx.c	2
		3024.2.cx.d	2
		3024.2.cx.e	2
		3024.2.cx.f	2
		3024.2.cx.g	2
		3024.2.cx.h	2
		3024.2.cx.i	24
		3024.2.cx.j	24
		3024.2.cx.k	32
3024.2.cy	\(\chi_{3024}(793, \cdot)\)	None	0	2
3024.2.cz	\(\chi_{3024}(1279, \cdot)\)	3024.2.cz.a	2	2
		3024.2.cz.b	2
		3024.2.cz.c	2
		3024.2.cz.d	2
		3024.2.cz.e	4
		3024.2.cz.f	4
		3024.2.cz.g	24
		3024.2.cz.h	24
		3024.2.cz.i	32
3024.2.da	\(\chi_{3024}(505, \cdot)\)	None	0	2
3024.2.df	\(\chi_{3024}(17, \cdot)\)	3024.2.df.a	2	2
		3024.2.df.b	10
		3024.2.df.c	16
		3024.2.df.d	16
		3024.2.df.e	48
3024.2.dg	\(\chi_{3024}(359, \cdot)\)	None	0	2
3024.2.dh	\(\chi_{3024}(199, \cdot)\)	None	0	2
3024.2.dk	\(\chi_{3024}(337, \cdot)\)	n/a	648	6
3024.2.dl	\(\chi_{3024}(193, \cdot)\)	n/a	852	6
3024.2.dm	\(\chi_{3024}(529, \cdot)\)	n/a	852	6
3024.2.dn	\(\chi_{3024}(307, \cdot)\)	n/a	752	4
3024.2.dp	\(\chi_{3024}(827, \cdot)\)	n/a	576	4
3024.2.dr	\(\chi_{3024}(1045, \cdot)\)	n/a	752	4
3024.2.du	\(\chi_{3024}(341, \cdot)\)	n/a	752	4
3024.2.dv	\(\chi_{3024}(269, \cdot)\)	n/a	1024	4
3024.2.dx	\(\chi_{3024}(109, \cdot)\)	n/a	1024	4
3024.2.ea	\(\chi_{3024}(37, \cdot)\)	n/a	752	4
3024.2.eb	\(\chi_{3024}(773, \cdot)\)	n/a	752	4
3024.2.ed	\(\chi_{3024}(179, \cdot)\)	n/a	752	4
3024.2.ef	\(\chi_{3024}(1027, \cdot)\)	n/a	1024	4
3024.2.ei	\(\chi_{3024}(451, \cdot)\)	n/a	752	4
3024.2.ek	\(\chi_{3024}(611, \cdot)\)	n/a	752	4
3024.2.el	\(\chi_{3024}(107, \cdot)\)	n/a	1024	4
3024.2.en	\(\chi_{3024}(19, \cdot)\)	n/a	752	4
3024.2.ep	\(\chi_{3024}(125, \cdot)\)	n/a	752	4
3024.2.er	\(\chi_{3024}(253, \cdot)\)	n/a	576	4
3024.2.eu	\(\chi_{3024}(527, \cdot)\)	n/a	864	6
3024.2.ew	\(\chi_{3024}(103, \cdot)\)	None	0	6
3024.2.ex	\(\chi_{3024}(367, \cdot)\)	n/a	864	6
3024.2.ez	\(\chi_{3024}(23, \cdot)\)	None	0	6
3024.2.fb	\(\chi_{3024}(185, \cdot)\)	None	0	6
3024.2.ff	\(\chi_{3024}(41, \cdot)\)	None	0	6
3024.2.fi	\(\chi_{3024}(457, \cdot)\)	None	0	6
3024.2.fj	\(\chi_{3024}(209, \cdot)\)	n/a	852	6
3024.2.fl	\(\chi_{3024}(169, \cdot)\)	None	0	6
3024.2.fo	\(\chi_{3024}(689, \cdot)\)	n/a	852	6
3024.2.fp	\(\chi_{3024}(599, \cdot)\)	None	0	6
3024.2.fs	\(\chi_{3024}(223, \cdot)\)	n/a	864	6
3024.2.fu	\(\chi_{3024}(407, \cdot)\)	None	0	6
3024.2.fv	\(\chi_{3024}(31, \cdot)\)	n/a	864	6
3024.2.fy	\(\chi_{3024}(439, \cdot)\)	None	0	6
3024.2.fz	\(\chi_{3024}(239, \cdot)\)	n/a	648	6
3024.2.gb	\(\chi_{3024}(391, \cdot)\)	None	0	6
3024.2.ge	\(\chi_{3024}(95, \cdot)\)	n/a	864	6
3024.2.gg	\(\chi_{3024}(257, \cdot)\)	n/a	852	6
3024.2.gi	\(\chi_{3024}(25, \cdot)\)	None	0	6
3024.2.gk	\(\chi_{3024}(761, \cdot)\)	None	0	6
3024.2.gm	\(\chi_{3024}(115, \cdot)\)	n/a	6864	12
3024.2.gp	\(\chi_{3024}(11, \cdot)\)	n/a	6864	12
3024.2.gq	\(\chi_{3024}(205, \cdot)\)	n/a	6864	12
3024.2.gs	\(\chi_{3024}(85, \cdot)\)	n/a	5184	12
3024.2.gv	\(\chi_{3024}(293, \cdot)\)	n/a	6864	12
3024.2.gx	\(\chi_{3024}(173, \cdot)\)	n/a	6864	12
3024.2.gz	\(\chi_{3024}(139, \cdot)\)	n/a	6864	12
3024.2.hb	\(\chi_{3024}(187, \cdot)\)	n/a	6864	12
3024.2.hc	\(\chi_{3024}(347, \cdot)\)	n/a	6864	12
3024.2.he	\(\chi_{3024}(155, \cdot)\)	n/a	5184	12
3024.2.hh	\(\chi_{3024}(277, \cdot)\)	n/a	6864	12
3024.2.hi	\(\chi_{3024}(5, \cdot)\)	n/a	6864	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 40}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3024))\)\(^{\oplus 1}\)