Space of modular forms of level 1008 and weight 3

• Label: 1008.3
• Level: 1008
• Weight: 3
• Dimension: 23395
• Nonzero newspaces: 40
• Sturm bound: 165888
• Trace bound: 29

Defining parameters

Level:	\( N \)	=	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(165888\)
Trace bound:			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1008))\).

	Total	New	Old
Modular forms	56640	23801	32839
Cusp forms	53952	23395	30557
Eisenstein series	2688	406	2282

Trace form

23395 * q - 24 * q^2 - 24 * q^3 - 12 * q^4 - 15 * q^5 - 32 * q^6 - 4 * q^7 - 72 * q^8 + 8 * q^9 - 148 * q^10 + 11 * q^11 - 32 * q^12 - 80 * q^13 - 76 * q^14 - 126 * q^15 - 172 * q^16 - 285 * q^17 - 232 * q^18 - 197 * q^19 - 196 * q^20 - 91 * q^21 - 56 * q^22 - 89 * q^23 + 32 * q^24 + 197 * q^25 + 164 * q^26 - 168 * q^27 + 92 * q^28 + 140 * q^29 + 392 * q^30 + 91 * q^31 + 676 * q^32 + 42 * q^33 + 476 * q^34 - 267 * q^35 + 312 * q^36 - 359 * q^37 + 900 * q^38 - 294 * q^39 + 788 * q^40 - 48 * q^41 + 160 * q^42 - 692 * q^43 - 68 * q^44 + 282 * q^45 - 608 * q^46 + 279 * q^47 - 136 * q^48 + 42 * q^49 - 1136 * q^50 + 604 * q^51 - 1192 * q^52 + 107 * q^53 - 648 * q^54 + 796 * q^55 - 304 * q^56 + 608 * q^57 - 1248 * q^58 + 1243 * q^59 + 1000 * q^60 + 77 * q^61 + 1152 * q^62 + 303 * q^63 - 564 * q^64 + 292 * q^65 + 1168 * q^66 + 39 * q^67 + 584 * q^68 - 526 * q^69 + 656 * q^70 - 718 * q^71 - 256 * q^72 - 455 * q^73 - 180 * q^74 - 776 * q^75 + 828 * q^76 - 1082 * q^77 - 1160 * q^78 + 595 * q^79 + 348 * q^80 - 1592 * q^81 + 2980 * q^82 + 548 * q^83 - 568 * q^84 - 418 * q^85 + 108 * q^86 + 534 * q^87 + 1652 * q^88 + 3 * q^89 - 608 * q^90 + 50 * q^91 + 1156 * q^92 - 234 * q^93 + 1356 * q^94 - 951 * q^95 - 168 * q^96 + 72 * q^97 + 512 * q^98 - 414 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1008))\)

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
1008.3.d	\(\chi_{1008}(449, \cdot)\)	1008.3.d.a	4	1
		1008.3.d.b	4
		1008.3.d.c	4
		1008.3.d.d	4
		1008.3.d.e	8
1008.3.e	\(\chi_{1008}(503, \cdot)\)	None	0	1
1008.3.f	\(\chi_{1008}(433, \cdot)\)	1008.3.f.a	1	1
		1008.3.f.b	2
		1008.3.f.c	2
		1008.3.f.d	2
		1008.3.f.e	2
		1008.3.f.f	2
		1008.3.f.g	4
		1008.3.f.h	4
		1008.3.f.i	4
		1008.3.f.j	8
		1008.3.f.k	8
1008.3.g	\(\chi_{1008}(631, \cdot)\)	None	0	1
1008.3.l	\(\chi_{1008}(937, \cdot)\)	None	0	1
1008.3.m	\(\chi_{1008}(127, \cdot)\)	1008.3.m.a	2	1
		1008.3.m.b	4
		1008.3.m.c	4
		1008.3.m.d	4
		1008.3.m.e	4
		1008.3.m.f	4
		1008.3.m.g	8
1008.3.n	\(\chi_{1008}(953, \cdot)\)	None	0	1
1008.3.o	\(\chi_{1008}(1007, \cdot)\)	1008.3.o.a	8	1
		1008.3.o.b	24
1008.3.u	\(\chi_{1008}(181, \cdot)\)	n/a	316	2
1008.3.w	\(\chi_{1008}(197, \cdot)\)	n/a	192	2
1008.3.y	\(\chi_{1008}(251, \cdot)\)	n/a	256	2
1008.3.ba	\(\chi_{1008}(379, \cdot)\)	n/a	240	2
1008.3.bc	\(\chi_{1008}(311, \cdot)\)	None	0	2
1008.3.bd	\(\chi_{1008}(65, \cdot)\)	n/a	188	2
1008.3.bi	\(\chi_{1008}(583, \cdot)\)	None	0	2
1008.3.bj	\(\chi_{1008}(817, \cdot)\)	n/a	188	2
1008.3.bk	\(\chi_{1008}(143, \cdot)\)	1008.3.bk.a	20	2
		1008.3.bk.b	20
		1008.3.bk.c	24
1008.3.bl	\(\chi_{1008}(233, \cdot)\)	None	0	2
1008.3.bo	\(\chi_{1008}(281, \cdot)\)	None	0	2
1008.3.bp	\(\chi_{1008}(383, \cdot)\)	n/a	192	2
1008.3.bq	\(\chi_{1008}(137, \cdot)\)	None	0	2
1008.3.br	\(\chi_{1008}(335, \cdot)\)	n/a	192	2
1008.3.bv	\(\chi_{1008}(265, \cdot)\)	None	0	2
1008.3.bw	\(\chi_{1008}(655, \cdot)\)	n/a	192	2
1008.3.bx	\(\chi_{1008}(745, \cdot)\)	None	0	2
1008.3.by	\(\chi_{1008}(463, \cdot)\)	n/a	144	2
1008.3.cd	\(\chi_{1008}(415, \cdot)\)	1008.3.cd.a	2	2
		1008.3.cd.b	2
		1008.3.cd.c	2
		1008.3.cd.d	2
		1008.3.cd.e	4
		1008.3.cd.f	4
		1008.3.cd.g	4
		1008.3.cd.h	6
		1008.3.cd.i	6
		1008.3.cd.j	6
		1008.3.cd.k	6
		1008.3.cd.l	6
		1008.3.cd.m	6
		1008.3.cd.n	8
		1008.3.cd.o	8
		1008.3.cd.p	8
1008.3.ce	\(\chi_{1008}(73, \cdot)\)	None	0	2
1008.3.cf	\(\chi_{1008}(487, \cdot)\)	None	0	2
1008.3.cg	\(\chi_{1008}(145, \cdot)\)	1008.3.cg.a	2	2
		1008.3.cg.b	2
		1008.3.cg.c	2
		1008.3.cg.d	2
		1008.3.cg.e	2
		1008.3.cg.f	2
		1008.3.cg.g	2
		1008.3.cg.h	4
		1008.3.cg.i	4
		1008.3.cg.j	4
		1008.3.cg.k	4
		1008.3.cg.l	4
		1008.3.cg.m	4
		1008.3.cg.n	8
		1008.3.cg.o	8
		1008.3.cg.p	8
		1008.3.cg.q	16
1008.3.cl	\(\chi_{1008}(97, \cdot)\)	n/a	188	2
1008.3.cm	\(\chi_{1008}(151, \cdot)\)	None	0	2
1008.3.cn	\(\chi_{1008}(241, \cdot)\)	n/a	188	2
1008.3.co	\(\chi_{1008}(295, \cdot)\)	None	0	2
1008.3.ct	\(\chi_{1008}(113, \cdot)\)	n/a	144	2
1008.3.cu	\(\chi_{1008}(887, \cdot)\)	None	0	2
1008.3.cv	\(\chi_{1008}(401, \cdot)\)	n/a	188	2
1008.3.cw	\(\chi_{1008}(167, \cdot)\)	None	0	2
1008.3.db	\(\chi_{1008}(215, \cdot)\)	None	0	2
1008.3.dc	\(\chi_{1008}(305, \cdot)\)	1008.3.dc.a	4	2
		1008.3.dc.b	4
		1008.3.dc.c	4
		1008.3.dc.d	8
		1008.3.dc.e	12
		1008.3.dc.f	16
		1008.3.dc.g	16
1008.3.dd	\(\chi_{1008}(79, \cdot)\)	n/a	192	2
1008.3.de	\(\chi_{1008}(313, \cdot)\)	None	0	2
1008.3.di	\(\chi_{1008}(47, \cdot)\)	n/a	192	2
1008.3.dj	\(\chi_{1008}(473, \cdot)\)	None	0	2
1008.3.dl	\(\chi_{1008}(29, \cdot)\)	n/a	1152	4
1008.3.dn	\(\chi_{1008}(13, \cdot)\)	n/a	1520	4
1008.3.dp	\(\chi_{1008}(59, \cdot)\)	n/a	1520	4
1008.3.dq	\(\chi_{1008}(403, \cdot)\)	n/a	1520	4
1008.3.dt	\(\chi_{1008}(163, \cdot)\)	n/a	632	4
1008.3.dv	\(\chi_{1008}(395, \cdot)\)	n/a	512	4
1008.3.dw	\(\chi_{1008}(131, \cdot)\)	n/a	1520	4
1008.3.dz	\(\chi_{1008}(67, \cdot)\)	n/a	1520	4
1008.3.eb	\(\chi_{1008}(61, \cdot)\)	n/a	1520	4
1008.3.ed	\(\chi_{1008}(53, \cdot)\)	n/a	512	4
1008.3.ee	\(\chi_{1008}(149, \cdot)\)	n/a	1520	4
1008.3.eg	\(\chi_{1008}(229, \cdot)\)	n/a	1520	4
1008.3.ej	\(\chi_{1008}(325, \cdot)\)	n/a	632	4
1008.3.el	\(\chi_{1008}(221, \cdot)\)	n/a	1520	4
1008.3.en	\(\chi_{1008}(43, \cdot)\)	n/a	1152	4
1008.3.ep	\(\chi_{1008}(83, \cdot)\)	n/a	1520	4

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1008))\) into lower level spaces

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