Space of modular forms of level 1008 and weight 5

• Label: 1008.5
• Level: 1008
• Weight: 5
• Dimension: 46993
• Nonzero newspaces: 40
• Sturm bound: 276480
• Trace bound: 29

Defining parameters

Level:	\( N \)	=	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(276480\)
Trace bound:			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(1008))\).

	Total	New	Old
Modular forms	111936	47399	64537
Cusp forms	109248	46993	62255
Eisenstein series	2688	406	2282

Trace form

46993 * q - 24 * q^2 - 24 * q^3 - 12 * q^4 - 99 * q^5 - 32 * q^6 + 12 * q^7 + 120 * q^8 - 232 * q^9 + 124 * q^10 - 213 * q^11 - 32 * q^12 - 36 * q^13 - 204 * q^14 + 450 * q^15 - 3500 * q^16 - 129 * q^17 + 2168 * q^18 + 2347 * q^19 + 6588 * q^20 + 1085 * q^21 + 2264 * q^22 - 4497 * q^23 - 3040 * q^24 - 5649 * q^25 - 9708 * q^26 - 3768 * q^27 - 3748 * q^28 - 1152 * q^29 - 4216 * q^30 + 971 * q^31 + 5796 * q^32 + 9498 * q^33 + 3612 * q^34 - 5499 * q^35 + 14904 * q^36 - 3603 * q^37 - 2124 * q^38 - 5046 * q^39 - 17516 * q^40 - 660 * q^41 - 11840 * q^42 + 40708 * q^43 - 29892 * q^44 + 8538 * q^45 + 4592 * q^46 + 25911 * q^47 + 9848 * q^48 + 42968 * q^49 + 48336 * q^50 - 41396 * q^51 + 40408 * q^52 - 31977 * q^53 + 36312 * q^54 - 55940 * q^55 + 29520 * q^56 + 28880 * q^57 - 15168 * q^58 + 36939 * q^59 - 33944 * q^60 + 11417 * q^61 - 140304 * q^62 + 9975 * q^63 + 12300 * q^64 - 28860 * q^65 - 128432 * q^66 + 1055 * q^67 - 54072 * q^68 - 51694 * q^69 + 52544 * q^70 - 31614 * q^71 + 32000 * q^72 - 4539 * q^73 + 94236 * q^74 + 63736 * q^75 - 12996 * q^76 + 99126 * q^77 + 209848 * q^78 + 102971 * q^79 + 207324 * q^80 + 95704 * q^81 - 89820 * q^82 + 8148 * q^83 - 30136 * q^84 + 40134 * q^85 - 224388 * q^86 - 151098 * q^87 - 95372 * q^88 - 136881 * q^89 - 216608 * q^90 - 153038 * q^91 - 94140 * q^92 - 35754 * q^93 + 87084 * q^94 - 128607 * q^95 + 25944 * q^96 + 17860 * q^97 + 54096 * q^98 + 178434 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(1008))\)

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
1008.5.d	\(\chi_{1008}(449, \cdot)\)	1008.5.d.a	4	1
		1008.5.d.b	4
		1008.5.d.c	8
		1008.5.d.d	8
		1008.5.d.e	12
		1008.5.d.f	12
1008.5.e	\(\chi_{1008}(503, \cdot)\)	None	0	1
1008.5.f	\(\chi_{1008}(433, \cdot)\)	1008.5.f.a	1	1
		1008.5.f.b	2
		1008.5.f.c	2
		1008.5.f.d	2
		1008.5.f.e	4
		1008.5.f.f	4
		1008.5.f.g	4
		1008.5.f.h	4
		1008.5.f.i	4
		1008.5.f.j	6
		1008.5.f.k	6
		1008.5.f.l	8
		1008.5.f.m	16
		1008.5.f.n	16
1008.5.g	\(\chi_{1008}(631, \cdot)\)	None	0	1
1008.5.l	\(\chi_{1008}(937, \cdot)\)	None	0	1
1008.5.m	\(\chi_{1008}(127, \cdot)\)	1008.5.m.a	4	1
		1008.5.m.b	8
		1008.5.m.c	8
		1008.5.m.d	8
		1008.5.m.e	8
		1008.5.m.f	8
		1008.5.m.g	16
1008.5.n	\(\chi_{1008}(953, \cdot)\)	None	0	1
1008.5.o	\(\chi_{1008}(1007, \cdot)\)	1008.5.o.a	24	1
		1008.5.o.b	40
1008.5.u	\(\chi_{1008}(181, \cdot)\)	n/a	636	2
1008.5.w	\(\chi_{1008}(197, \cdot)\)	n/a	384	2
1008.5.y	\(\chi_{1008}(251, \cdot)\)	n/a	512	2
1008.5.ba	\(\chi_{1008}(379, \cdot)\)	n/a	480	2
1008.5.bc	\(\chi_{1008}(311, \cdot)\)	None	0	2
1008.5.bd	\(\chi_{1008}(65, \cdot)\)	n/a	380	2
1008.5.bi	\(\chi_{1008}(583, \cdot)\)	None	0	2
1008.5.bj	\(\chi_{1008}(817, \cdot)\)	n/a	380	2
1008.5.bk	\(\chi_{1008}(143, \cdot)\)	n/a	128	2
1008.5.bl	\(\chi_{1008}(233, \cdot)\)	None	0	2
1008.5.bo	\(\chi_{1008}(281, \cdot)\)	None	0	2
1008.5.bp	\(\chi_{1008}(383, \cdot)\)	n/a	384	2
1008.5.bq	\(\chi_{1008}(137, \cdot)\)	None	0	2
1008.5.br	\(\chi_{1008}(335, \cdot)\)	n/a	384	2
1008.5.bv	\(\chi_{1008}(265, \cdot)\)	None	0	2
1008.5.bw	\(\chi_{1008}(655, \cdot)\)	n/a	384	2
1008.5.bx	\(\chi_{1008}(745, \cdot)\)	None	0	2
1008.5.by	\(\chi_{1008}(463, \cdot)\)	n/a	288	2
1008.5.cd	\(\chi_{1008}(415, \cdot)\)	n/a	160	2
1008.5.ce	\(\chi_{1008}(73, \cdot)\)	None	0	2
1008.5.cf	\(\chi_{1008}(487, \cdot)\)	None	0	2
1008.5.cg	\(\chi_{1008}(145, \cdot)\)	n/a	158	2
1008.5.cl	\(\chi_{1008}(97, \cdot)\)	n/a	380	2
1008.5.cm	\(\chi_{1008}(151, \cdot)\)	None	0	2
1008.5.cn	\(\chi_{1008}(241, \cdot)\)	n/a	380	2
1008.5.co	\(\chi_{1008}(295, \cdot)\)	None	0	2
1008.5.ct	\(\chi_{1008}(113, \cdot)\)	n/a	288	2
1008.5.cu	\(\chi_{1008}(887, \cdot)\)	None	0	2
1008.5.cv	\(\chi_{1008}(401, \cdot)\)	n/a	380	2
1008.5.cw	\(\chi_{1008}(167, \cdot)\)	None	0	2
1008.5.db	\(\chi_{1008}(215, \cdot)\)	None	0	2
1008.5.dc	\(\chi_{1008}(305, \cdot)\)	n/a	128	2
1008.5.dd	\(\chi_{1008}(79, \cdot)\)	n/a	384	2
1008.5.de	\(\chi_{1008}(313, \cdot)\)	None	0	2
1008.5.di	\(\chi_{1008}(47, \cdot)\)	n/a	384	2
1008.5.dj	\(\chi_{1008}(473, \cdot)\)	None	0	2
1008.5.dl	\(\chi_{1008}(29, \cdot)\)	n/a	2304	4
1008.5.dn	\(\chi_{1008}(13, \cdot)\)	n/a	3056	4
1008.5.dp	\(\chi_{1008}(59, \cdot)\)	n/a	3056	4
1008.5.dq	\(\chi_{1008}(403, \cdot)\)	n/a	3056	4
1008.5.dt	\(\chi_{1008}(163, \cdot)\)	n/a	1272	4
1008.5.dv	\(\chi_{1008}(395, \cdot)\)	n/a	1024	4
1008.5.dw	\(\chi_{1008}(131, \cdot)\)	n/a	3056	4
1008.5.dz	\(\chi_{1008}(67, \cdot)\)	n/a	3056	4
1008.5.eb	\(\chi_{1008}(61, \cdot)\)	n/a	3056	4
1008.5.ed	\(\chi_{1008}(53, \cdot)\)	n/a	1024	4
1008.5.ee	\(\chi_{1008}(149, \cdot)\)	n/a	3056	4
1008.5.eg	\(\chi_{1008}(229, \cdot)\)	n/a	3056	4
1008.5.ej	\(\chi_{1008}(325, \cdot)\)	n/a	1272	4
1008.5.el	\(\chi_{1008}(221, \cdot)\)	n/a	3056	4
1008.5.en	\(\chi_{1008}(43, \cdot)\)	n/a	2304	4
1008.5.ep	\(\chi_{1008}(83, \cdot)\)	n/a	3056	4

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(1008))\) into lower level spaces

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