Space of modular forms of level 2448 and weight 4

• Label: 2448.4
• Level: 2448
• Weight: 4
• Dimension: 219470
• Nonzero newspaces: 52
• Sturm bound: 1327104
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 52 \)
Sturm bound:			\(1327104\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2448))\).

	Total	New	Old
Modular forms	501248	220684	280564
Cusp forms	494080	219470	274610
Eisenstein series	7168	1214	5954

Trace form

219470 * q - 84 * q^2 - 84 * q^3 - 104 * q^4 - 106 * q^5 - 112 * q^6 - 90 * q^7 + 12 * q^9 - 120 * q^10 + 78 * q^11 - 112 * q^12 - 6 * q^13 - 336 * q^14 - 42 * q^15 + 408 * q^16 - 100 * q^17 + 40 * q^18 - 460 * q^19 - 928 * q^20 - 738 * q^21 - 928 * q^22 - 710 * q^23 - 1584 * q^24 - 1374 * q^25 - 1736 * q^26 + 672 * q^27 - 1104 * q^28 + 454 * q^29 + 888 * q^30 - 294 * q^31 + 1896 * q^32 - 162 * q^33 + 864 * q^34 + 972 * q^35 - 1640 * q^36 + 1560 * q^37 - 2440 * q^38 + 366 * q^39 + 1432 * q^40 + 210 * q^41 + 1248 * q^42 - 3026 * q^43 + 4336 * q^44 + 386 * q^45 + 3368 * q^46 - 7698 * q^47 + 4776 * q^48 - 3170 * q^49 + 7116 * q^50 - 2050 * q^51 + 3744 * q^52 - 1156 * q^53 + 328 * q^54 - 476 * q^55 - 5856 * q^56 - 2328 * q^57 - 4616 * q^58 + 8378 * q^59 - 15976 * q^60 + 3802 * q^61 - 9552 * q^62 + 4998 * q^63 - 3440 * q^64 + 7486 * q^65 + 9728 * q^66 - 2534 * q^67 + 3344 * q^68 + 5406 * q^69 - 7032 * q^70 - 1000 * q^71 + 15792 * q^72 - 9428 * q^73 + 8096 * q^74 + 964 * q^75 - 2528 * q^76 + 9054 * q^77 + 920 * q^78 - 874 * q^79 - 13472 * q^80 + 700 * q^81 - 7152 * q^82 - 5334 * q^83 - 19216 * q^84 + 1386 * q^85 - 17792 * q^86 + 402 * q^87 + 9528 * q^88 - 1632 * q^89 - 2416 * q^90 + 10524 * q^91 + 24904 * q^92 - 1882 * q^93 + 24136 * q^94 + 2672 * q^95 + 12808 * q^96 - 5306 * q^97 + 28852 * q^98 + 3054 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2448))\)

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
2448.4.a	\(\chi_{2448}(1, \cdot)\)	2448.4.a.a	1	1
		2448.4.a.b	1
		2448.4.a.c	1
		2448.4.a.d	1
		2448.4.a.e	1
		2448.4.a.f	1
		2448.4.a.g	1
		2448.4.a.h	1
		2448.4.a.i	1
		2448.4.a.j	1
		2448.4.a.k	1
		2448.4.a.l	1
		2448.4.a.m	1
		2448.4.a.n	1
		2448.4.a.o	1
		2448.4.a.p	1
		2448.4.a.q	1
		2448.4.a.r	1
		2448.4.a.s	2
		2448.4.a.t	2
		2448.4.a.u	2
		2448.4.a.v	2
		2448.4.a.w	2
		2448.4.a.x	2
		2448.4.a.y	2
		2448.4.a.z	2
		2448.4.a.ba	3
		2448.4.a.bb	3
		2448.4.a.bc	3
		2448.4.a.bd	3
		2448.4.a.be	3
		2448.4.a.bf	3
		2448.4.a.bg	3
		2448.4.a.bh	3
		2448.4.a.bi	3
		2448.4.a.bj	3
		2448.4.a.bk	3
		2448.4.a.bl	3
		2448.4.a.bm	3
		2448.4.a.bn	3
		2448.4.a.bo	4
		2448.4.a.bp	4
		2448.4.a.bq	4
		2448.4.a.br	4
		2448.4.a.bs	4
		2448.4.a.bt	5
		2448.4.a.bu	5
		2448.4.a.bv	7
		2448.4.a.bw	7
2448.4.c	\(\chi_{2448}(577, \cdot)\)	n/a	134	1
2448.4.e	\(\chi_{2448}(1871, \cdot)\)	2448.4.e.a	32	1
		2448.4.e.b	64
2448.4.f	\(\chi_{2448}(1225, \cdot)\)	None	0	1
2448.4.h	\(\chi_{2448}(1223, \cdot)\)	None	0	1
2448.4.j	\(\chi_{2448}(647, \cdot)\)	None	0	1
2448.4.l	\(\chi_{2448}(1801, \cdot)\)	None	0	1
2448.4.o	\(\chi_{2448}(2447, \cdot)\)	n/a	108	1
2448.4.q	\(\chi_{2448}(817, \cdot)\)	n/a	576	2
2448.4.s	\(\chi_{2448}(395, \cdot)\)	n/a	864	2
2448.4.t	\(\chi_{2448}(973, \cdot)\)	n/a	1076	2
2448.4.v	\(\chi_{2448}(613, \cdot)\)	n/a	960	2
2448.4.x	\(\chi_{2448}(611, \cdot)\)	n/a	864	2
2448.4.z	\(\chi_{2448}(2087, \cdot)\)	None	0	2
2448.4.bb	\(\chi_{2448}(217, \cdot)\)	None	0	2
2448.4.be	\(\chi_{2448}(1441, \cdot)\)	n/a	268	2
2448.4.bg	\(\chi_{2448}(863, \cdot)\)	n/a	216	2
2448.4.bi	\(\chi_{2448}(35, \cdot)\)	n/a	768	2
2448.4.bk	\(\chi_{2448}(1189, \cdot)\)	n/a	1076	2
2448.4.bm	\(\chi_{2448}(829, \cdot)\)	n/a	1076	2
2448.4.bn	\(\chi_{2448}(251, \cdot)\)	n/a	864	2
2448.4.bq	\(\chi_{2448}(815, \cdot)\)	n/a	648	2
2448.4.bt	\(\chi_{2448}(169, \cdot)\)	None	0	2
2448.4.bv	\(\chi_{2448}(1463, \cdot)\)	None	0	2
2448.4.bx	\(\chi_{2448}(407, \cdot)\)	None	0	2
2448.4.bz	\(\chi_{2448}(409, \cdot)\)	None	0	2
2448.4.ca	\(\chi_{2448}(239, \cdot)\)	n/a	576	2
2448.4.cc	\(\chi_{2448}(1393, \cdot)\)	n/a	644	2
2448.4.cg	\(\chi_{2448}(145, \cdot)\)	n/a	536	4
2448.4.ch	\(\chi_{2448}(287, \cdot)\)	n/a	432	4
2448.4.ci	\(\chi_{2448}(179, \cdot)\)	n/a	1728	4
2448.4.cj	\(\chi_{2448}(253, \cdot)\)	n/a	2152	4
2448.4.cm	\(\chi_{2448}(899, \cdot)\)	n/a	1728	4
2448.4.cn	\(\chi_{2448}(325, \cdot)\)	n/a	2152	4
2448.4.cq	\(\chi_{2448}(937, \cdot)\)	None	0	4
2448.4.cr	\(\chi_{2448}(359, \cdot)\)	None	0	4
2448.4.cu	\(\chi_{2448}(803, \cdot)\)	n/a	5168	4
2448.4.cx	\(\chi_{2448}(13, \cdot)\)	n/a	5168	4
2448.4.cy	\(\chi_{2448}(373, \cdot)\)	n/a	5168	4
2448.4.da	\(\chi_{2448}(443, \cdot)\)	n/a	4608	4
2448.4.dd	\(\chi_{2448}(625, \cdot)\)	n/a	1288	4
2448.4.df	\(\chi_{2448}(47, \cdot)\)	n/a	1296	4
2448.4.dg	\(\chi_{2448}(455, \cdot)\)	None	0	4
2448.4.di	\(\chi_{2448}(1033, \cdot)\)	None	0	4
2448.4.dl	\(\chi_{2448}(203, \cdot)\)	n/a	5168	4
2448.4.dn	\(\chi_{2448}(205, \cdot)\)	n/a	4608	4
2448.4.do	\(\chi_{2448}(157, \cdot)\)	n/a	5168	4
2448.4.dr	\(\chi_{2448}(659, \cdot)\)	n/a	5168	4
2448.4.dt	\(\chi_{2448}(197, \cdot)\)	n/a	3456	8
2448.4.du	\(\chi_{2448}(91, \cdot)\)	n/a	4304	8
2448.4.dx	\(\chi_{2448}(449, \cdot)\)	n/a	864	8
2448.4.dy	\(\chi_{2448}(415, \cdot)\)	n/a	1080	8
2448.4.eb	\(\chi_{2448}(199, \cdot)\)	None	0	8
2448.4.ec	\(\chi_{2448}(233, \cdot)\)	None	0	8
2448.4.ef	\(\chi_{2448}(125, \cdot)\)	n/a	3456	8
2448.4.eg	\(\chi_{2448}(163, \cdot)\)	n/a	4304	8
2448.4.ei	\(\chi_{2448}(25, \cdot)\)	None	0	8
2448.4.ej	\(\chi_{2448}(263, \cdot)\)	None	0	8
2448.4.eo	\(\chi_{2448}(155, \cdot)\)	n/a	10336	8
2448.4.ep	\(\chi_{2448}(229, \cdot)\)	n/a	10336	8
2448.4.es	\(\chi_{2448}(59, \cdot)\)	n/a	10336	8
2448.4.et	\(\chi_{2448}(349, \cdot)\)	n/a	10336	8
2448.4.ew	\(\chi_{2448}(49, \cdot)\)	n/a	2576	8
2448.4.ex	\(\chi_{2448}(383, \cdot)\)	n/a	2592	8
2448.4.ez	\(\chi_{2448}(139, \cdot)\)	n/a	20672	16
2448.4.fa	\(\chi_{2448}(5, \cdot)\)	n/a	20672	16
2448.4.fd	\(\chi_{2448}(31, \cdot)\)	n/a	5184	16
2448.4.fe	\(\chi_{2448}(65, \cdot)\)	n/a	5152	16
2448.4.fh	\(\chi_{2448}(41, \cdot)\)	None	0	16
2448.4.fi	\(\chi_{2448}(7, \cdot)\)	None	0	16
2448.4.fl	\(\chi_{2448}(283, \cdot)\)	n/a	20672	16
2448.4.fm	\(\chi_{2448}(29, \cdot)\)	n/a	20672	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2448))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2448)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2448))\)\(^{\oplus 1}\)