Space of modular forms of level 1248 and weight 4

• Label: 1248.4
• Level: 1248
• Weight: 4
• Dimension: 53564
• Nonzero newspaces: 40
• Sturm bound: 344064
• Trace bound: 28

Defining parameters

Level:	\( N \)	=	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(344064\)
Trace bound:			\(28\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1248))\).

	Total	New	Old
Modular forms	130560	54004	76556
Cusp forms	127488	53564	73924
Eisenstein series	3072	440	2632

Trace form

53564 * q - 32 * q^3 - 80 * q^4 + 8 * q^5 - 40 * q^6 - 20 * q^9 + 400 * q^10 - 136 * q^12 - 324 * q^13 - 832 * q^14 - 140 * q^15 - 1280 * q^16 - 416 * q^17 - 184 * q^18 - 112 * q^19 + 320 * q^20 - 72 * q^21 + 704 * q^22 + 1968 * q^23 - 128 * q^24 + 556 * q^25 + 40 * q^26 - 860 * q^27 + 1440 * q^28 - 568 * q^29 + 2216 * q^30 - 4320 * q^31 + 2480 * q^32 - 184 * q^33 + 2048 * q^34 - 1824 * q^35 - 1200 * q^36 + 1240 * q^37 - 880 * q^38 + 880 * q^39 - 3456 * q^40 + 2128 * q^41 - 1840 * q^42 + 4032 * q^43 - 2000 * q^44 + 1120 * q^45 - 80 * q^46 - 816 * q^47 + 4848 * q^48 - 1452 * q^49 - 5712 * q^50 - 1272 * q^51 - 3400 * q^52 + 3432 * q^53 - 32 * q^54 + 840 * q^55 + 784 * q^56 + 1480 * q^57 + 4672 * q^58 + 5504 * q^59 - 736 * q^60 - 5640 * q^61 + 5856 * q^62 + 1476 * q^63 + 19744 * q^64 + 2024 * q^65 + 11912 * q^66 + 4832 * q^67 + 10064 * q^68 - 4776 * q^69 + 5536 * q^70 - 2512 * q^71 - 2800 * q^72 - 9736 * q^73 - 13888 * q^74 - 9036 * q^75 - 20560 * q^76 - 128 * q^77 - 6892 * q^78 - 11528 * q^79 - 22672 * q^80 - 8124 * q^81 - 11760 * q^82 - 4864 * q^84 + 14624 * q^85 - 4736 * q^86 + 16804 * q^87 - 1312 * q^88 + 20544 * q^89 - 5680 * q^90 + 13280 * q^91 + 15392 * q^92 + 11328 * q^93 + 33184 * q^94 + 2768 * q^95 + 9712 * q^96 + 3496 * q^97 + 20576 * q^98 + 2884 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1248))\)

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
1248.4.a	\(\chi_{1248}(1, \cdot)\)	1248.4.a.a	3	1
		1248.4.a.b	3
		1248.4.a.c	4
		1248.4.a.d	4
		1248.4.a.e	4
		1248.4.a.f	4
		1248.4.a.g	5
		1248.4.a.h	5
		1248.4.a.i	5
		1248.4.a.j	5
		1248.4.a.k	5
		1248.4.a.l	5
		1248.4.a.m	5
		1248.4.a.n	5
		1248.4.a.o	5
		1248.4.a.p	5
1248.4.c	\(\chi_{1248}(961, \cdot)\)	1248.4.c.a	20	1
		1248.4.c.b	20
		1248.4.c.c	22
		1248.4.c.d	22
1248.4.d	\(\chi_{1248}(287, \cdot)\)	n/a	144	1
1248.4.g	\(\chi_{1248}(625, \cdot)\)	1248.4.g.a	32	1
		1248.4.g.b	40
1248.4.h	\(\chi_{1248}(623, \cdot)\)	n/a	164	1
1248.4.j	\(\chi_{1248}(911, \cdot)\)	n/a	144	1
1248.4.m	\(\chi_{1248}(337, \cdot)\)	1248.4.m.a	84	1
1248.4.n	\(\chi_{1248}(1247, \cdot)\)	n/a	168	1
1248.4.q	\(\chi_{1248}(289, \cdot)\)	n/a	168	2
1248.4.r	\(\chi_{1248}(343, \cdot)\)	None	0	2
1248.4.u	\(\chi_{1248}(473, \cdot)\)	None	0	2
1248.4.v	\(\chi_{1248}(311, \cdot)\)	None	0	2
1248.4.x	\(\chi_{1248}(313, \cdot)\)	None	0	2
1248.4.bb	\(\chi_{1248}(463, \cdot)\)	n/a	168	2
1248.4.bc	\(\chi_{1248}(31, \cdot)\)	n/a	168	2
1248.4.bf	\(\chi_{1248}(161, \cdot)\)	n/a	336	2
1248.4.bg	\(\chi_{1248}(593, \cdot)\)	n/a	328	2
1248.4.bh	\(\chi_{1248}(599, \cdot)\)	None	0	2
1248.4.bj	\(\chi_{1248}(25, \cdot)\)	None	0	2
1248.4.bm	\(\chi_{1248}(281, \cdot)\)	None	0	2
1248.4.bn	\(\chi_{1248}(151, \cdot)\)	None	0	2
1248.4.bq	\(\chi_{1248}(335, \cdot)\)	n/a	328	2
1248.4.br	\(\chi_{1248}(529, \cdot)\)	n/a	168	2
1248.4.bu	\(\chi_{1248}(191, \cdot)\)	n/a	336	2
1248.4.bv	\(\chi_{1248}(673, \cdot)\)	n/a	168	2
1248.4.bz	\(\chi_{1248}(95, \cdot)\)	n/a	336	2
1248.4.ca	\(\chi_{1248}(49, \cdot)\)	n/a	168	2
1248.4.cd	\(\chi_{1248}(815, \cdot)\)	n/a	328	2
1248.4.cf	\(\chi_{1248}(5, \cdot)\)	n/a	2672	4
1248.4.ch	\(\chi_{1248}(499, \cdot)\)	n/a	1344	4
1248.4.ci	\(\chi_{1248}(181, \cdot)\)	n/a	1344	4
1248.4.ck	\(\chi_{1248}(157, \cdot)\)	n/a	1152	4
1248.4.cn	\(\chi_{1248}(131, \cdot)\)	n/a	2304	4
1248.4.cp	\(\chi_{1248}(155, \cdot)\)	n/a	2672	4
1248.4.cq	\(\chi_{1248}(317, \cdot)\)	n/a	2672	4
1248.4.cs	\(\chi_{1248}(187, \cdot)\)	n/a	1344	4
1248.4.cu	\(\chi_{1248}(137, \cdot)\)	None	0	4
1248.4.cx	\(\chi_{1248}(7, \cdot)\)	None	0	4
1248.4.cz	\(\chi_{1248}(121, \cdot)\)	None	0	4
1248.4.db	\(\chi_{1248}(263, \cdot)\)	None	0	4
1248.4.dc	\(\chi_{1248}(305, \cdot)\)	n/a	656	4
1248.4.dd	\(\chi_{1248}(353, \cdot)\)	n/a	672	4
1248.4.dg	\(\chi_{1248}(223, \cdot)\)	n/a	336	4
1248.4.dh	\(\chi_{1248}(175, \cdot)\)	n/a	336	4
1248.4.dl	\(\chi_{1248}(217, \cdot)\)	None	0	4
1248.4.dn	\(\chi_{1248}(23, \cdot)\)	None	0	4
1248.4.dp	\(\chi_{1248}(487, \cdot)\)	None	0	4
1248.4.dq	\(\chi_{1248}(41, \cdot)\)	None	0	4
1248.4.dt	\(\chi_{1248}(115, \cdot)\)	n/a	2688	8
1248.4.dv	\(\chi_{1248}(245, \cdot)\)	n/a	5344	8
1248.4.dx	\(\chi_{1248}(35, \cdot)\)	n/a	5344	8
1248.4.dz	\(\chi_{1248}(179, \cdot)\)	n/a	5344	8
1248.4.ea	\(\chi_{1248}(205, \cdot)\)	n/a	2688	8
1248.4.ec	\(\chi_{1248}(61, \cdot)\)	n/a	2688	8
1248.4.ee	\(\chi_{1248}(19, \cdot)\)	n/a	2688	8
1248.4.eg	\(\chi_{1248}(149, \cdot)\)	n/a	5344	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1248))\) into lower level spaces

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