Space of modular forms of level 1008 and weight 2

• Label: 1008.2
• Level: 1008
• Weight: 2
• Dimension: 11597
• Nonzero newspaces: 40
• Sturm bound: 110592
• Trace bound: 29

Defining parameters

Level:	\( N \)	=	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(110592\)
Trace bound:			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1008))\).

	Total	New	Old
Modular forms	28992	12001	16991
Cusp forms	26305	11597	14708
Eisenstein series	2687	404	2283

Trace form

11597 * q - 24 * q^2 - 24 * q^3 - 28 * q^4 - 35 * q^5 - 32 * q^6 - 28 * q^7 - 72 * q^8 - 16 * q^9 - 76 * q^10 - 45 * q^11 - 32 * q^12 - 50 * q^13 - 12 * q^14 - 66 * q^15 + 20 * q^16 - 37 * q^17 + 8 * q^18 - 67 * q^19 + 76 * q^20 - 37 * q^21 + 32 * q^22 + 5 * q^23 + 32 * q^24 + 23 * q^25 + 92 * q^26 + 12 * q^27 - 52 * q^28 - 28 * q^29 + 8 * q^30 - 17 * q^31 + 36 * q^32 - 30 * q^33 - 4 * q^34 + 33 * q^35 - 72 * q^36 - 119 * q^37 - 116 * q^38 + 90 * q^39 - 140 * q^40 + 30 * q^41 - 80 * q^42 + 78 * q^43 - 148 * q^44 + 6 * q^45 - 136 * q^46 + 141 * q^47 - 136 * q^48 - 60 * q^49 - 144 * q^50 + 40 * q^51 - 40 * q^52 + 35 * q^53 - 120 * q^54 + 114 * q^55 - 48 * q^56 - 64 * q^57 - 16 * q^58 + 55 * q^59 - 248 * q^60 + 65 * q^61 - 120 * q^62 - 33 * q^63 + 44 * q^64 - 150 * q^65 - 272 * q^66 - 5 * q^67 - 136 * q^68 - 142 * q^69 + 56 * q^70 - 68 * q^71 - 256 * q^72 + 85 * q^73 - 140 * q^74 - 20 * q^75 + 44 * q^76 + 62 * q^77 - 296 * q^78 + 17 * q^79 - 292 * q^80 - 128 * q^81 - 92 * q^82 - 72 * q^83 - 184 * q^84 + 130 * q^85 - 316 * q^86 - 54 * q^87 - 172 * q^88 + 99 * q^89 - 320 * q^90 + 80 * q^91 - 268 * q^92 + 138 * q^93 - 292 * q^94 + 25 * q^95 - 168 * q^96 + 38 * q^97 - 248 * q^98 - 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)

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
1008.2.a	\(\chi_{1008}(1, \cdot)\)	1008.2.a.a	1	1
		1008.2.a.b	1
		1008.2.a.c	1
		1008.2.a.d	1
		1008.2.a.e	1
		1008.2.a.f	1
		1008.2.a.g	1
		1008.2.a.h	1
		1008.2.a.i	1
		1008.2.a.j	1
		1008.2.a.k	1
		1008.2.a.l	1
		1008.2.a.m	1
		1008.2.a.n	2
1008.2.b	\(\chi_{1008}(559, \cdot)\)	1008.2.b.a	2	1
		1008.2.b.b	2
		1008.2.b.c	2
		1008.2.b.d	2
		1008.2.b.e	2
		1008.2.b.f	2
		1008.2.b.g	2
		1008.2.b.h	2
		1008.2.b.i	4
1008.2.c	\(\chi_{1008}(505, \cdot)\)	None	0	1
1008.2.h	\(\chi_{1008}(575, \cdot)\)	1008.2.h.a	4	1
		1008.2.h.b	8
1008.2.i	\(\chi_{1008}(377, \cdot)\)	None	0	1
1008.2.j	\(\chi_{1008}(71, \cdot)\)	None	0	1
1008.2.k	\(\chi_{1008}(881, \cdot)\)	1008.2.k.a	4	1
		1008.2.k.b	4
		1008.2.k.c	8
1008.2.p	\(\chi_{1008}(55, \cdot)\)	None	0	1
1008.2.q	\(\chi_{1008}(529, \cdot)\)	1008.2.q.a	2	2
		1008.2.q.b	2
		1008.2.q.c	2
		1008.2.q.d	2
		1008.2.q.e	2
		1008.2.q.f	2
		1008.2.q.g	6
		1008.2.q.h	6
		1008.2.q.i	10
		1008.2.q.j	14
		1008.2.q.k	22
		1008.2.q.l	22
1008.2.r	\(\chi_{1008}(337, \cdot)\)	1008.2.r.a	2	2
		1008.2.r.b	2
		1008.2.r.c	2
		1008.2.r.d	2
		1008.2.r.e	4
		1008.2.r.f	4
		1008.2.r.g	6
		1008.2.r.h	6
		1008.2.r.i	6
		1008.2.r.j	6
		1008.2.r.k	6
		1008.2.r.l	8
		1008.2.r.m	8
		1008.2.r.n	10
1008.2.s	\(\chi_{1008}(289, \cdot)\)	1008.2.s.a	2	2
		1008.2.s.b	2
		1008.2.s.c	2
		1008.2.s.d	2
		1008.2.s.e	2
		1008.2.s.f	2
		1008.2.s.g	2
		1008.2.s.h	2
		1008.2.s.i	2
		1008.2.s.j	2
		1008.2.s.k	2
		1008.2.s.l	2
		1008.2.s.m	2
		1008.2.s.n	2
		1008.2.s.o	2
		1008.2.s.p	2
		1008.2.s.q	2
		1008.2.s.r	4
1008.2.t	\(\chi_{1008}(193, \cdot)\)	1008.2.t.a	2	2
		1008.2.t.b	2
		1008.2.t.c	2
		1008.2.t.d	2
		1008.2.t.e	2
		1008.2.t.f	2
		1008.2.t.g	6
		1008.2.t.h	6
		1008.2.t.i	10
		1008.2.t.j	14
		1008.2.t.k	22
		1008.2.t.l	22
1008.2.v	\(\chi_{1008}(323, \cdot)\)	1008.2.v.a	4	2
		1008.2.v.b	4
		1008.2.v.c	12
		1008.2.v.d	36
		1008.2.v.e	40
1008.2.x	\(\chi_{1008}(307, \cdot)\)	n/a	156	2
1008.2.z	\(\chi_{1008}(253, \cdot)\)	n/a	120	2
1008.2.bb	\(\chi_{1008}(125, \cdot)\)	n/a	128	2
1008.2.be	\(\chi_{1008}(457, \cdot)\)	None	0	2
1008.2.bf	\(\chi_{1008}(31, \cdot)\)	1008.2.bf.a	2	2
		1008.2.bf.b	2
		1008.2.bf.c	2
		1008.2.bf.d	2
		1008.2.bf.e	4
		1008.2.bf.f	4
		1008.2.bf.g	24
		1008.2.bf.h	24
		1008.2.bf.i	32
1008.2.bg	\(\chi_{1008}(185, \cdot)\)	None	0	2
1008.2.bh	\(\chi_{1008}(95, \cdot)\)	1008.2.bh.a	2	2
		1008.2.bh.b	2
		1008.2.bh.c	30
		1008.2.bh.d	30
		1008.2.bh.e	32
1008.2.bm	\(\chi_{1008}(391, \cdot)\)	None	0	2
1008.2.bn	\(\chi_{1008}(103, \cdot)\)	None	0	2
1008.2.bs	\(\chi_{1008}(199, \cdot)\)	None	0	2
1008.2.bt	\(\chi_{1008}(17, \cdot)\)	1008.2.bt.a	4	2
		1008.2.bt.b	4
		1008.2.bt.c	8
		1008.2.bt.d	16
1008.2.bu	\(\chi_{1008}(359, \cdot)\)	None	0	2
1008.2.bz	\(\chi_{1008}(407, \cdot)\)	None	0	2
1008.2.ca	\(\chi_{1008}(257, \cdot)\)	1008.2.ca.a	2	2
		1008.2.ca.b	10
		1008.2.ca.c	16
		1008.2.ca.d	16
		1008.2.ca.e	48
1008.2.cb	\(\chi_{1008}(23, \cdot)\)	None	0	2
1008.2.cc	\(\chi_{1008}(209, \cdot)\)	1008.2.cc.a	12	2
		1008.2.cc.b	16
		1008.2.cc.c	16
		1008.2.cc.d	48
1008.2.ch	\(\chi_{1008}(239, \cdot)\)	1008.2.ch.a	24	2
		1008.2.ch.b	24
		1008.2.ch.c	24
1008.2.ci	\(\chi_{1008}(761, \cdot)\)	None	0	2
1008.2.cj	\(\chi_{1008}(527, \cdot)\)	1008.2.cj.a	2	2
		1008.2.cj.b	2
		1008.2.cj.c	30
		1008.2.cj.d	30
		1008.2.cj.e	32
1008.2.ck	\(\chi_{1008}(41, \cdot)\)	None	0	2
1008.2.cp	\(\chi_{1008}(89, \cdot)\)	None	0	2
1008.2.cq	\(\chi_{1008}(431, \cdot)\)	1008.2.cq.a	8	2
		1008.2.cq.b	12
		1008.2.cq.c	12
1008.2.cr	\(\chi_{1008}(361, \cdot)\)	None	0	2
1008.2.cs	\(\chi_{1008}(271, \cdot)\)	1008.2.cs.a	2	2
		1008.2.cs.b	2
		1008.2.cs.c	2
		1008.2.cs.d	2
		1008.2.cs.e	2
		1008.2.cs.f	2
		1008.2.cs.g	2
		1008.2.cs.h	2
		1008.2.cs.i	2
		1008.2.cs.j	2
		1008.2.cs.k	2
		1008.2.cs.l	2
		1008.2.cs.m	2
		1008.2.cs.n	2
		1008.2.cs.o	4
		1008.2.cs.p	4
		1008.2.cs.q	4
1008.2.cx	\(\chi_{1008}(223, \cdot)\)	1008.2.cx.a	2	2
		1008.2.cx.b	2
		1008.2.cx.c	2
		1008.2.cx.d	2
		1008.2.cx.e	2
		1008.2.cx.f	2
		1008.2.cx.g	2
		1008.2.cx.h	2
		1008.2.cx.i	24
		1008.2.cx.j	24
		1008.2.cx.k	32
1008.2.cy	\(\chi_{1008}(25, \cdot)\)	None	0	2
1008.2.cz	\(\chi_{1008}(367, \cdot)\)	1008.2.cz.a	2	2
		1008.2.cz.b	2
		1008.2.cz.c	2
		1008.2.cz.d	2
		1008.2.cz.e	4
		1008.2.cz.f	4
		1008.2.cz.g	24
		1008.2.cz.h	24
		1008.2.cz.i	32
1008.2.da	\(\chi_{1008}(169, \cdot)\)	None	0	2
1008.2.df	\(\chi_{1008}(689, \cdot)\)	1008.2.df.a	2	2
		1008.2.df.b	10
		1008.2.df.c	16
		1008.2.df.d	16
		1008.2.df.e	48
1008.2.dg	\(\chi_{1008}(599, \cdot)\)	None	0	2
1008.2.dh	\(\chi_{1008}(439, \cdot)\)	None	0	2
1008.2.dk	\(\chi_{1008}(139, \cdot)\)	n/a	752	4
1008.2.dm	\(\chi_{1008}(155, \cdot)\)	n/a	576	4
1008.2.do	\(\chi_{1008}(205, \cdot)\)	n/a	752	4
1008.2.dr	\(\chi_{1008}(5, \cdot)\)	n/a	752	4
1008.2.ds	\(\chi_{1008}(269, \cdot)\)	n/a	256	4
1008.2.du	\(\chi_{1008}(37, \cdot)\)	n/a	312	4
1008.2.dx	\(\chi_{1008}(277, \cdot)\)	n/a	752	4
1008.2.dy	\(\chi_{1008}(173, \cdot)\)	n/a	752	4
1008.2.ea	\(\chi_{1008}(347, \cdot)\)	n/a	752	4
1008.2.ec	\(\chi_{1008}(19, \cdot)\)	n/a	312	4
1008.2.ef	\(\chi_{1008}(115, \cdot)\)	n/a	752	4
1008.2.eh	\(\chi_{1008}(11, \cdot)\)	n/a	752	4
1008.2.ei	\(\chi_{1008}(107, \cdot)\)	n/a	256	4
1008.2.ek	\(\chi_{1008}(187, \cdot)\)	n/a	752	4
1008.2.em	\(\chi_{1008}(293, \cdot)\)	n/a	752	4
1008.2.eo	\(\chi_{1008}(85, \cdot)\)	n/a	576	4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1008))\) into lower level spaces

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