Space of modular forms of level 2448 and weight 2

• Label: 2448.2
• Level: 2448
• Weight: 2
• Dimension: 72752
• Nonzero newspaces: 52
• Sturm bound: 663552
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 52 \)
Sturm bound:			\(663552\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2448))\).

	Total	New	Old
Modular forms	169472	73966	95506
Cusp forms	162305	72752	89553
Eisenstein series	7167	1214	5953

Trace form

72752 * q - 84 * q^2 - 84 * q^3 - 88 * q^4 - 110 * q^5 - 112 * q^6 - 74 * q^7 - 96 * q^8 - 36 * q^9 - 256 * q^10 - 90 * q^11 - 112 * q^12 - 122 * q^13 - 48 * q^14 - 90 * q^15 - 40 * q^16 - 194 * q^17 - 200 * q^18 - 196 * q^19 + 16 * q^20 - 114 * q^21 + 8 * q^22 - 22 * q^23 - 48 * q^24 + 32 * q^25 + 32 * q^26 - 48 * q^27 - 176 * q^28 - 46 * q^29 - 72 * q^30 - 38 * q^31 - 24 * q^32 - 210 * q^33 - 80 * q^34 + 12 * q^35 - 104 * q^36 - 332 * q^37 - 176 * q^38 + 30 * q^39 - 200 * q^40 + 6 * q^41 - 192 * q^42 + 54 * q^43 - 256 * q^44 - 94 * q^45 - 376 * q^46 + 78 * q^47 - 216 * q^48 - 256 * q^49 - 252 * q^50 - 58 * q^51 - 304 * q^52 - 104 * q^53 - 200 * q^54 - 108 * q^55 - 288 * q^56 - 72 * q^57 - 160 * q^58 - 62 * q^59 - 328 * q^60 - 122 * q^61 - 288 * q^62 - 90 * q^63 - 112 * q^64 - 442 * q^65 - 352 * q^66 - 126 * q^67 - 176 * q^68 - 450 * q^69 - 8 * q^70 - 248 * q^71 - 336 * q^72 - 96 * q^73 - 200 * q^74 - 188 * q^75 - 16 * q^76 - 258 * q^77 - 328 * q^78 - 202 * q^79 - 352 * q^80 - 404 * q^81 - 272 * q^82 - 318 * q^83 - 400 * q^84 - 98 * q^85 - 472 * q^86 - 222 * q^87 - 232 * q^88 - 60 * q^89 - 400 * q^90 - 356 * q^91 - 280 * q^92 - 58 * q^93 - 280 * q^94 - 272 * q^95 - 248 * q^96 - 166 * q^97 - 268 * q^98 - 114 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2448))\)

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
2448.2.a	\(\chi_{2448}(1, \cdot)\)	2448.2.a.a	1	1
		2448.2.a.b	1
		2448.2.a.c	1
		2448.2.a.d	1
		2448.2.a.e	1
		2448.2.a.f	1
		2448.2.a.g	1
		2448.2.a.h	1
		2448.2.a.i	1
		2448.2.a.j	1
		2448.2.a.k	1
		2448.2.a.l	1
		2448.2.a.m	1
		2448.2.a.n	1
		2448.2.a.o	1
		2448.2.a.p	1
		2448.2.a.q	1
		2448.2.a.r	1
		2448.2.a.s	1
		2448.2.a.t	1
		2448.2.a.u	2
		2448.2.a.v	2
		2448.2.a.w	2
		2448.2.a.x	2
		2448.2.a.y	2
		2448.2.a.z	2
		2448.2.a.ba	2
		2448.2.a.bb	3
		2448.2.a.bc	3
2448.2.c	\(\chi_{2448}(577, \cdot)\)	2448.2.c.a	2	1
		2448.2.c.b	2
		2448.2.c.c	2
		2448.2.c.d	2
		2448.2.c.e	2
		2448.2.c.f	2
		2448.2.c.g	2
		2448.2.c.h	2
		2448.2.c.i	2
		2448.2.c.j	2
		2448.2.c.k	2
		2448.2.c.l	2
		2448.2.c.m	2
		2448.2.c.n	2
		2448.2.c.o	2
		2448.2.c.p	4
		2448.2.c.q	4
		2448.2.c.r	6
2448.2.e	\(\chi_{2448}(1871, \cdot)\)	2448.2.e.a	8	1
		2448.2.e.b	24
2448.2.f	\(\chi_{2448}(1225, \cdot)\)	None	0	1
2448.2.h	\(\chi_{2448}(1223, \cdot)\)	None	0	1
2448.2.j	\(\chi_{2448}(647, \cdot)\)	None	0	1
2448.2.l	\(\chi_{2448}(1801, \cdot)\)	None	0	1
2448.2.o	\(\chi_{2448}(2447, \cdot)\)	2448.2.o.a	4	1
		2448.2.o.b	4
		2448.2.o.c	4
		2448.2.o.d	24
2448.2.q	\(\chi_{2448}(817, \cdot)\)	n/a	192	2
2448.2.s	\(\chi_{2448}(395, \cdot)\)	n/a	288	2
2448.2.t	\(\chi_{2448}(973, \cdot)\)	n/a	356	2
2448.2.v	\(\chi_{2448}(613, \cdot)\)	n/a	320	2
2448.2.x	\(\chi_{2448}(611, \cdot)\)	n/a	288	2
2448.2.z	\(\chi_{2448}(2087, \cdot)\)	None	0	2
2448.2.bb	\(\chi_{2448}(217, \cdot)\)	None	0	2
2448.2.be	\(\chi_{2448}(1441, \cdot)\)	2448.2.be.a	2	2
		2448.2.be.b	2
		2448.2.be.c	2
		2448.2.be.d	2
		2448.2.be.e	2
		2448.2.be.f	2
		2448.2.be.g	2
		2448.2.be.h	2
		2448.2.be.i	2
		2448.2.be.j	2
		2448.2.be.k	2
		2448.2.be.l	2
		2448.2.be.m	2
		2448.2.be.n	2
		2448.2.be.o	4
		2448.2.be.p	4
		2448.2.be.q	4
		2448.2.be.r	4
		2448.2.be.s	4
		2448.2.be.t	4
		2448.2.be.u	4
		2448.2.be.v	6
		2448.2.be.w	6
		2448.2.be.x	8
		2448.2.be.y	12
2448.2.bg	\(\chi_{2448}(863, \cdot)\)	2448.2.bg.a	4	2
		2448.2.bg.b	4
		2448.2.bg.c	8
		2448.2.bg.d	8
		2448.2.bg.e	8
		2448.2.bg.f	40
2448.2.bi	\(\chi_{2448}(35, \cdot)\)	n/a	256	2
2448.2.bk	\(\chi_{2448}(1189, \cdot)\)	n/a	356	2
2448.2.bm	\(\chi_{2448}(829, \cdot)\)	n/a	356	2
2448.2.bn	\(\chi_{2448}(251, \cdot)\)	n/a	288	2
2448.2.bq	\(\chi_{2448}(815, \cdot)\)	n/a	216	2
2448.2.bt	\(\chi_{2448}(169, \cdot)\)	None	0	2
2448.2.bv	\(\chi_{2448}(1463, \cdot)\)	None	0	2
2448.2.bx	\(\chi_{2448}(407, \cdot)\)	None	0	2
2448.2.bz	\(\chi_{2448}(409, \cdot)\)	None	0	2
2448.2.ca	\(\chi_{2448}(239, \cdot)\)	n/a	192	2
2448.2.cc	\(\chi_{2448}(1393, \cdot)\)	n/a	212	2
2448.2.cg	\(\chi_{2448}(145, \cdot)\)	n/a	176	4
2448.2.ch	\(\chi_{2448}(287, \cdot)\)	n/a	144	4
2448.2.ci	\(\chi_{2448}(179, \cdot)\)	n/a	576	4
2448.2.cj	\(\chi_{2448}(253, \cdot)\)	n/a	712	4
2448.2.cm	\(\chi_{2448}(899, \cdot)\)	n/a	576	4
2448.2.cn	\(\chi_{2448}(325, \cdot)\)	n/a	712	4
2448.2.cq	\(\chi_{2448}(937, \cdot)\)	None	0	4
2448.2.cr	\(\chi_{2448}(359, \cdot)\)	None	0	4
2448.2.cu	\(\chi_{2448}(803, \cdot)\)	n/a	1712	4
2448.2.cx	\(\chi_{2448}(13, \cdot)\)	n/a	1712	4
2448.2.cy	\(\chi_{2448}(373, \cdot)\)	n/a	1712	4
2448.2.da	\(\chi_{2448}(443, \cdot)\)	n/a	1536	4
2448.2.dd	\(\chi_{2448}(625, \cdot)\)	n/a	424	4
2448.2.df	\(\chi_{2448}(47, \cdot)\)	n/a	432	4
2448.2.dg	\(\chi_{2448}(455, \cdot)\)	None	0	4
2448.2.di	\(\chi_{2448}(1033, \cdot)\)	None	0	4
2448.2.dl	\(\chi_{2448}(203, \cdot)\)	n/a	1712	4
2448.2.dn	\(\chi_{2448}(205, \cdot)\)	n/a	1536	4
2448.2.do	\(\chi_{2448}(157, \cdot)\)	n/a	1712	4
2448.2.dr	\(\chi_{2448}(659, \cdot)\)	n/a	1712	4
2448.2.dt	\(\chi_{2448}(197, \cdot)\)	n/a	1152	8
2448.2.du	\(\chi_{2448}(91, \cdot)\)	n/a	1424	8
2448.2.dx	\(\chi_{2448}(449, \cdot)\)	n/a	288	8
2448.2.dy	\(\chi_{2448}(415, \cdot)\)	n/a	360	8
2448.2.eb	\(\chi_{2448}(199, \cdot)\)	None	0	8
2448.2.ec	\(\chi_{2448}(233, \cdot)\)	None	0	8
2448.2.ef	\(\chi_{2448}(125, \cdot)\)	n/a	1152	8
2448.2.eg	\(\chi_{2448}(163, \cdot)\)	n/a	1424	8
2448.2.ei	\(\chi_{2448}(25, \cdot)\)	None	0	8
2448.2.ej	\(\chi_{2448}(263, \cdot)\)	None	0	8
2448.2.eo	\(\chi_{2448}(155, \cdot)\)	n/a	3424	8
2448.2.ep	\(\chi_{2448}(229, \cdot)\)	n/a	3424	8
2448.2.es	\(\chi_{2448}(59, \cdot)\)	n/a	3424	8
2448.2.et	\(\chi_{2448}(349, \cdot)\)	n/a	3424	8
2448.2.ew	\(\chi_{2448}(49, \cdot)\)	n/a	848	8
2448.2.ex	\(\chi_{2448}(383, \cdot)\)	n/a	864	8
2448.2.ez	\(\chi_{2448}(139, \cdot)\)	n/a	6848	16
2448.2.fa	\(\chi_{2448}(5, \cdot)\)	n/a	6848	16
2448.2.fd	\(\chi_{2448}(31, \cdot)\)	n/a	1728	16
2448.2.fe	\(\chi_{2448}(65, \cdot)\)	n/a	1696	16
2448.2.fh	\(\chi_{2448}(41, \cdot)\)	None	0	16
2448.2.fi	\(\chi_{2448}(7, \cdot)\)	None	0	16
2448.2.fl	\(\chi_{2448}(283, \cdot)\)	n/a	6848	16
2448.2.fm	\(\chi_{2448}(29, \cdot)\)	n/a	6848	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2448))\) into lower level spaces

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