Space of modular forms of level 1248 and weight 2

• Label: 1248.2
• Level: 1248
• Weight: 2
• Dimension: 17708
• Nonzero newspaces: 40
• Sturm bound: 172032
• Trace bound: 28

Defining parameters

Level:	\( N \)	=	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(172032\)
Trace bound:			\(28\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1248))\).

	Total	New	Old
Modular forms	44544	18148	26396
Cusp forms	41473	17708	23765
Eisenstein series	3071	440	2631

Trace form

17708 * q - 32 * q^3 - 80 * q^4 - 8 * q^5 - 40 * q^6 - 64 * q^7 - 68 * q^9 - 48 * q^10 - 8 * q^12 - 76 * q^13 + 64 * q^14 - 12 * q^15 + 32 * q^17 - 24 * q^18 - 48 * q^19 + 64 * q^20 - 8 * q^21 - 32 * q^22 + 48 * q^23 - 64 * q^24 - 84 * q^25 - 40 * q^26 + 4 * q^27 - 160 * q^28 - 8 * q^29 - 136 * q^30 + 32 * q^31 - 80 * q^32 - 104 * q^33 - 128 * q^34 + 96 * q^35 - 144 * q^36 - 120 * q^37 - 80 * q^38 - 16 * q^39 - 256 * q^40 - 16 * q^41 - 160 * q^42 - 64 * q^43 - 16 * q^44 - 112 * q^45 - 80 * q^46 - 48 * q^47 - 144 * q^48 - 124 * q^49 - 48 * q^50 - 56 * q^51 - 136 * q^52 + 24 * q^53 - 144 * q^54 - 184 * q^55 - 112 * q^56 - 104 * q^57 - 224 * q^58 - 128 * q^59 - 160 * q^60 + 40 * q^61 - 96 * q^62 - 60 * q^63 - 224 * q^64 - 8 * q^65 - 136 * q^66 - 160 * q^67 + 16 * q^68 + 88 * q^69 - 128 * q^70 - 80 * q^71 + 80 * q^72 - 40 * q^73 + 64 * q^74 - 76 * q^75 - 80 * q^76 + 128 * q^77 + 20 * q^78 - 136 * q^79 + 112 * q^80 + 52 * q^81 + 80 * q^82 + 224 * q^84 + 96 * q^85 + 128 * q^86 - 92 * q^87 + 96 * q^88 + 192 * q^89 + 224 * q^90 + 128 * q^91 + 160 * q^92 + 128 * q^93 + 96 * q^94 + 208 * q^95 + 240 * q^96 + 8 * q^97 + 160 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)

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
1248.2.a	\(\chi_{1248}(1, \cdot)\)	1248.2.a.a	1	1
		1248.2.a.b	1
		1248.2.a.c	1
		1248.2.a.d	1
		1248.2.a.e	1
		1248.2.a.f	1
		1248.2.a.g	1
		1248.2.a.h	1
		1248.2.a.i	1
		1248.2.a.j	1
		1248.2.a.k	2
		1248.2.a.l	2
		1248.2.a.m	2
		1248.2.a.n	2
		1248.2.a.o	3
		1248.2.a.p	3
1248.2.c	\(\chi_{1248}(961, \cdot)\)	1248.2.c.a	6	1
		1248.2.c.b	6
		1248.2.c.c	8
		1248.2.c.d	8
1248.2.d	\(\chi_{1248}(287, \cdot)\)	1248.2.d.a	4	1
		1248.2.d.b	8
		1248.2.d.c	16
		1248.2.d.d	20
1248.2.g	\(\chi_{1248}(625, \cdot)\)	1248.2.g.a	8	1
		1248.2.g.b	16
1248.2.h	\(\chi_{1248}(623, \cdot)\)	1248.2.h.a	8	1
		1248.2.h.b	12
		1248.2.h.c	32
1248.2.j	\(\chi_{1248}(911, \cdot)\)	1248.2.j.a	48	1
1248.2.m	\(\chi_{1248}(337, \cdot)\)	1248.2.m.a	2	1
		1248.2.m.b	2
		1248.2.m.c	24
1248.2.n	\(\chi_{1248}(1247, \cdot)\)	1248.2.n.a	4	1
		1248.2.n.b	4
		1248.2.n.c	4
		1248.2.n.d	4
		1248.2.n.e	40
1248.2.q	\(\chi_{1248}(289, \cdot)\)	1248.2.q.a	2	2
		1248.2.q.b	2
		1248.2.q.c	2
		1248.2.q.d	2
		1248.2.q.e	2
		1248.2.q.f	2
		1248.2.q.g	4
		1248.2.q.h	4
		1248.2.q.i	4
		1248.2.q.j	4
		1248.2.q.k	6
		1248.2.q.l	6
		1248.2.q.m	8
		1248.2.q.n	8
1248.2.r	\(\chi_{1248}(343, \cdot)\)	None	0	2
1248.2.u	\(\chi_{1248}(473, \cdot)\)	None	0	2
1248.2.v	\(\chi_{1248}(311, \cdot)\)	None	0	2
1248.2.x	\(\chi_{1248}(313, \cdot)\)	None	0	2
1248.2.bb	\(\chi_{1248}(463, \cdot)\)	1248.2.bb.a	2	2
		1248.2.bb.b	2
		1248.2.bb.c	2
		1248.2.bb.d	2
		1248.2.bb.e	24
		1248.2.bb.f	24
1248.2.bc	\(\chi_{1248}(31, \cdot)\)	1248.2.bc.a	2	2
		1248.2.bc.b	2
		1248.2.bc.c	2
		1248.2.bc.d	2
		1248.2.bc.e	2
		1248.2.bc.f	2
		1248.2.bc.g	2
		1248.2.bc.h	2
		1248.2.bc.i	2
		1248.2.bc.j	2
		1248.2.bc.k	2
		1248.2.bc.l	2
		1248.2.bc.m	2
		1248.2.bc.n	2
		1248.2.bc.o	4
		1248.2.bc.p	4
		1248.2.bc.q	4
		1248.2.bc.r	4
		1248.2.bc.s	6
		1248.2.bc.t	6
1248.2.bf	\(\chi_{1248}(161, \cdot)\)	n/a	112	2
1248.2.bg	\(\chi_{1248}(593, \cdot)\)	n/a	104	2
1248.2.bh	\(\chi_{1248}(599, \cdot)\)	None	0	2
1248.2.bj	\(\chi_{1248}(25, \cdot)\)	None	0	2
1248.2.bm	\(\chi_{1248}(281, \cdot)\)	None	0	2
1248.2.bn	\(\chi_{1248}(151, \cdot)\)	None	0	2
1248.2.bq	\(\chi_{1248}(335, \cdot)\)	n/a	104	2
1248.2.br	\(\chi_{1248}(529, \cdot)\)	1248.2.br.a	56	2
1248.2.bu	\(\chi_{1248}(191, \cdot)\)	n/a	112	2
1248.2.bv	\(\chi_{1248}(673, \cdot)\)	1248.2.bv.a	12	2
		1248.2.bv.b	12
		1248.2.bv.c	16
		1248.2.bv.d	16
1248.2.bz	\(\chi_{1248}(95, \cdot)\)	n/a	112	2
1248.2.ca	\(\chi_{1248}(49, \cdot)\)	1248.2.ca.a	8	2
		1248.2.ca.b	48
1248.2.cd	\(\chi_{1248}(815, \cdot)\)	n/a	104	2
1248.2.cf	\(\chi_{1248}(5, \cdot)\)	n/a	880	4
1248.2.ch	\(\chi_{1248}(499, \cdot)\)	n/a	448	4
1248.2.ci	\(\chi_{1248}(181, \cdot)\)	n/a	448	4
1248.2.ck	\(\chi_{1248}(157, \cdot)\)	n/a	384	4
1248.2.cn	\(\chi_{1248}(131, \cdot)\)	n/a	768	4
1248.2.cp	\(\chi_{1248}(155, \cdot)\)	n/a	880	4
1248.2.cq	\(\chi_{1248}(317, \cdot)\)	n/a	880	4
1248.2.cs	\(\chi_{1248}(187, \cdot)\)	n/a	448	4
1248.2.cu	\(\chi_{1248}(137, \cdot)\)	None	0	4
1248.2.cx	\(\chi_{1248}(7, \cdot)\)	None	0	4
1248.2.cz	\(\chi_{1248}(121, \cdot)\)	None	0	4
1248.2.db	\(\chi_{1248}(263, \cdot)\)	None	0	4
1248.2.dc	\(\chi_{1248}(305, \cdot)\)	n/a	208	4
1248.2.dd	\(\chi_{1248}(353, \cdot)\)	n/a	224	4
1248.2.dg	\(\chi_{1248}(223, \cdot)\)	n/a	112	4
1248.2.dh	\(\chi_{1248}(175, \cdot)\)	n/a	112	4
1248.2.dl	\(\chi_{1248}(217, \cdot)\)	None	0	4
1248.2.dn	\(\chi_{1248}(23, \cdot)\)	None	0	4
1248.2.dp	\(\chi_{1248}(487, \cdot)\)	None	0	4
1248.2.dq	\(\chi_{1248}(41, \cdot)\)	None	0	4
1248.2.dt	\(\chi_{1248}(115, \cdot)\)	n/a	896	8
1248.2.dv	\(\chi_{1248}(245, \cdot)\)	n/a	1760	8
1248.2.dx	\(\chi_{1248}(35, \cdot)\)	n/a	1760	8
1248.2.dz	\(\chi_{1248}(179, \cdot)\)	n/a	1760	8
1248.2.ea	\(\chi_{1248}(205, \cdot)\)	n/a	896	8
1248.2.ec	\(\chi_{1248}(61, \cdot)\)	n/a	896	8
1248.2.ee	\(\chi_{1248}(19, \cdot)\)	n/a	896	8
1248.2.eg	\(\chi_{1248}(149, \cdot)\)	n/a	1760	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1248)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 2}\)