Space of modular forms of level 1512 and weight 2

• Label: 1512.2
• Level: 1512
• Weight: 2
• Dimension: 26176
• Nonzero newspaces: 48
• Sturm bound: 248832
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(248832\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1512))\).

	Total	New	Old
Modular forms	64368	26816	37552
Cusp forms	60049	26176	33873
Eisenstein series	4319	640	3679

Trace form

26176 * q - 32 * q^2 - 48 * q^3 - 56 * q^4 + 4 * q^5 - 48 * q^6 - 70 * q^7 - 92 * q^8 - 96 * q^9 - 72 * q^10 - 56 * q^11 - 48 * q^12 - 20 * q^13 - 46 * q^14 - 144 * q^15 - 64 * q^16 - 116 * q^17 - 48 * q^18 - 88 * q^19 - 20 * q^20 - 12 * q^21 - 100 * q^22 - 84 * q^23 - 12 * q^24 - 134 * q^25 + 52 * q^26 - 18 * q^27 - 116 * q^28 + 60 * q^29 + 48 * q^30 - 28 * q^31 + 188 * q^32 - 78 * q^33 + 40 * q^34 + 6 * q^35 + 36 * q^37 + 188 * q^38 + 24 * q^39 + 64 * q^40 - 68 * q^41 - 92 * q^43 + 156 * q^44 + 108 * q^45 + 16 * q^46 + 84 * q^47 - 12 * q^48 - 190 * q^49 + 40 * q^50 + 72 * q^51 - 32 * q^52 + 16 * q^53 - 48 * q^54 - 88 * q^55 - 118 * q^56 - 150 * q^57 - 136 * q^58 + 142 * q^59 - 168 * q^60 + 28 * q^61 - 292 * q^62 + 36 * q^63 - 260 * q^64 + 68 * q^65 - 228 * q^66 + 68 * q^67 - 288 * q^68 + 96 * q^69 - 98 * q^70 + 236 * q^71 - 216 * q^72 - 72 * q^73 - 188 * q^74 + 84 * q^75 - 160 * q^76 + 96 * q^77 - 348 * q^78 + 116 * q^79 - 168 * q^80 - 72 * q^81 - 64 * q^82 + 212 * q^83 - 126 * q^84 + 80 * q^85 - 44 * q^86 - 36 * q^87 + 80 * q^88 - 110 * q^89 - 324 * q^90 + 36 * q^91 - 36 * q^92 - 144 * q^93 + 144 * q^94 - 20 * q^95 - 360 * q^96 - 72 * q^97 - 44 * q^98 - 396 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1512))\)

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
1512.2.a	\(\chi_{1512}(1, \cdot)\)	1512.2.a.a	1	1
		1512.2.a.b	1
		1512.2.a.c	1
		1512.2.a.d	1
		1512.2.a.e	1
		1512.2.a.f	1
		1512.2.a.g	1
		1512.2.a.h	1
		1512.2.a.i	1
		1512.2.a.j	1
		1512.2.a.k	1
		1512.2.a.l	1
		1512.2.a.m	2
		1512.2.a.n	2
		1512.2.a.o	2
		1512.2.a.p	2
		1512.2.a.q	2
		1512.2.a.r	2
1512.2.b	\(\chi_{1512}(55, \cdot)\)	None	0	1
1512.2.c	\(\chi_{1512}(757, \cdot)\)	1512.2.c.a	2	1
		1512.2.c.b	2
		1512.2.c.c	8
		1512.2.c.d	16
		1512.2.c.e	20
		1512.2.c.f	24
		1512.2.c.g	24
1512.2.h	\(\chi_{1512}(1079, \cdot)\)	None	0	1
1512.2.i	\(\chi_{1512}(1133, \cdot)\)	n/a	128	1
1512.2.j	\(\chi_{1512}(323, \cdot)\)	1512.2.j.a	8	1
		1512.2.j.b	8
		1512.2.j.c	32
		1512.2.j.d	48
1512.2.k	\(\chi_{1512}(377, \cdot)\)	1512.2.k.a	16	1
		1512.2.k.b	16
1512.2.p	\(\chi_{1512}(811, \cdot)\)	n/a	128	1
1512.2.q	\(\chi_{1512}(793, \cdot)\)	1512.2.q.a	2	2
		1512.2.q.b	2
		1512.2.q.c	22
		1512.2.q.d	22
1512.2.r	\(\chi_{1512}(505, \cdot)\)	1512.2.r.a	2	2
		1512.2.r.b	2
		1512.2.r.c	6
		1512.2.r.d	8
		1512.2.r.e	8
		1512.2.r.f	10
1512.2.s	\(\chi_{1512}(865, \cdot)\)	1512.2.s.a	2	2
		1512.2.s.b	2
		1512.2.s.c	2
		1512.2.s.d	2
		1512.2.s.e	2
		1512.2.s.f	2
		1512.2.s.g	2
		1512.2.s.h	2
		1512.2.s.i	2
		1512.2.s.j	2
		1512.2.s.k	6
		1512.2.s.l	6
		1512.2.s.m	8
		1512.2.s.n	8
		1512.2.s.o	8
		1512.2.s.p	8
1512.2.t	\(\chi_{1512}(289, \cdot)\)	1512.2.t.a	2	2
		1512.2.t.b	2
		1512.2.t.c	22
		1512.2.t.d	22
1512.2.w	\(\chi_{1512}(1045, \cdot)\)	n/a	184	2
1512.2.x	\(\chi_{1512}(199, \cdot)\)	None	0	2
1512.2.y	\(\chi_{1512}(773, \cdot)\)	n/a	184	2
1512.2.z	\(\chi_{1512}(359, \cdot)\)	None	0	2
1512.2.be	\(\chi_{1512}(307, \cdot)\)	n/a	184	2
1512.2.bf	\(\chi_{1512}(451, \cdot)\)	n/a	184	2
1512.2.bk	\(\chi_{1512}(1027, \cdot)\)	n/a	256	2
1512.2.bl	\(\chi_{1512}(593, \cdot)\)	1512.2.bl.a	16	2
		1512.2.bl.b	16
		1512.2.bl.c	16
		1512.2.bl.d	16
1512.2.bm	\(\chi_{1512}(107, \cdot)\)	n/a	256	2
1512.2.br	\(\chi_{1512}(827, \cdot)\)	n/a	144	2
1512.2.bs	\(\chi_{1512}(521, \cdot)\)	1512.2.bs.a	48	2
1512.2.bt	\(\chi_{1512}(611, \cdot)\)	n/a	184	2
1512.2.bu	\(\chi_{1512}(881, \cdot)\)	1512.2.bu.a	48	2
1512.2.bz	\(\chi_{1512}(71, \cdot)\)	None	0	2
1512.2.ca	\(\chi_{1512}(341, \cdot)\)	n/a	184	2
1512.2.cb	\(\chi_{1512}(1367, \cdot)\)	None	0	2
1512.2.cc	\(\chi_{1512}(125, \cdot)\)	n/a	184	2
1512.2.ch	\(\chi_{1512}(269, \cdot)\)	n/a	256	2
1512.2.ci	\(\chi_{1512}(431, \cdot)\)	None	0	2
1512.2.cj	\(\chi_{1512}(109, \cdot)\)	n/a	256	2
1512.2.ck	\(\chi_{1512}(271, \cdot)\)	None	0	2
1512.2.cp	\(\chi_{1512}(559, \cdot)\)	None	0	2
1512.2.cq	\(\chi_{1512}(37, \cdot)\)	n/a	184	2
1512.2.cr	\(\chi_{1512}(1207, \cdot)\)	None	0	2
1512.2.cs	\(\chi_{1512}(253, \cdot)\)	n/a	144	2
1512.2.cx	\(\chi_{1512}(17, \cdot)\)	1512.2.cx.a	48	2
1512.2.cy	\(\chi_{1512}(179, \cdot)\)	n/a	184	2
1512.2.cz	\(\chi_{1512}(19, \cdot)\)	n/a	184	2
1512.2.dc	\(\chi_{1512}(169, \cdot)\)	n/a	324	6
1512.2.dd	\(\chi_{1512}(193, \cdot)\)	n/a	432	6
1512.2.de	\(\chi_{1512}(25, \cdot)\)	n/a	432	6
1512.2.dg	\(\chi_{1512}(23, \cdot)\)	None	0	6
1512.2.di	\(\chi_{1512}(115, \cdot)\)	n/a	1704	6
1512.2.dj	\(\chi_{1512}(103, \cdot)\)	None	0	6
1512.2.dl	\(\chi_{1512}(11, \cdot)\)	n/a	1704	6
1512.2.dn	\(\chi_{1512}(173, \cdot)\)	n/a	1704	6
1512.2.dr	\(\chi_{1512}(293, \cdot)\)	n/a	1704	6
1512.2.du	\(\chi_{1512}(205, \cdot)\)	n/a	1704	6
1512.2.dv	\(\chi_{1512}(41, \cdot)\)	n/a	432	6
1512.2.dx	\(\chi_{1512}(85, \cdot)\)	n/a	1296	6
1512.2.ea	\(\chi_{1512}(185, \cdot)\)	n/a	432	6
1512.2.eb	\(\chi_{1512}(347, \cdot)\)	n/a	1704	6
1512.2.ee	\(\chi_{1512}(223, \cdot)\)	None	0	6
1512.2.eg	\(\chi_{1512}(155, \cdot)\)	n/a	1296	6
1512.2.eh	\(\chi_{1512}(31, \cdot)\)	None	0	6
1512.2.ek	\(\chi_{1512}(187, \cdot)\)	n/a	1704	6
1512.2.el	\(\chi_{1512}(239, \cdot)\)	None	0	6
1512.2.en	\(\chi_{1512}(139, \cdot)\)	n/a	1704	6
1512.2.eq	\(\chi_{1512}(95, \cdot)\)	None	0	6
1512.2.es	\(\chi_{1512}(257, \cdot)\)	n/a	432	6
1512.2.eu	\(\chi_{1512}(277, \cdot)\)	n/a	1704	6
1512.2.ew	\(\chi_{1512}(5, \cdot)\)	n/a	1704	6

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1512))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1512)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(756))\)\(^{\oplus 2}\)