Space of modular forms of level 2496 and weight 2

• Label: 2496.2
• Level: 2496
• Weight: 2
• Dimension: 71228
• Nonzero newspaces: 56
• Sturm bound: 688128
• Trace bound: 43

Defining parameters

Level:	\( N \)	=	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(688128\)
Trace bound:			\(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2496))\).

	Total	New	Old
Modular forms	175488	72196	103292
Cusp forms	168577	71228	97349
Eisenstein series	6911	968	5943

Trace form

71228 * q - 60 * q^3 - 160 * q^4 - 80 * q^6 - 128 * q^7 - 100 * q^9 - 160 * q^10 - 16 * q^11 - 80 * q^12 - 192 * q^13 - 72 * q^15 - 160 * q^16 - 32 * q^17 - 80 * q^18 - 152 * q^19 - 72 * q^21 - 128 * q^22 - 156 * q^25 + 80 * q^26 - 108 * q^27 + 64 * q^29 + 80 * q^30 - 32 * q^31 + 160 * q^32 + 16 * q^33 + 48 * q^35 + 80 * q^36 - 96 * q^37 + 160 * q^38 - 44 * q^39 - 192 * q^40 + 64 * q^41 - 104 * q^43 + 32 * q^44 + 8 * q^45 - 160 * q^46 - 80 * q^48 - 252 * q^49 - 96 * q^50 + 72 * q^51 - 272 * q^52 - 112 * q^54 + 192 * q^55 - 224 * q^56 - 48 * q^57 - 448 * q^58 + 320 * q^59 - 272 * q^60 - 160 * q^61 - 192 * q^62 + 8 * q^63 - 544 * q^64 + 16 * q^65 - 336 * q^66 + 232 * q^67 - 192 * q^68 - 152 * q^69 - 544 * q^70 + 256 * q^71 - 80 * q^72 - 200 * q^73 - 224 * q^74 + 36 * q^75 - 416 * q^76 - 96 * q^77 - 160 * q^78 - 176 * q^79 - 96 * q^80 - 268 * q^81 - 160 * q^82 - 80 * q^83 - 304 * q^84 - 256 * q^85 - 176 * q^87 - 160 * q^88 - 64 * q^89 - 368 * q^90 - 192 * q^91 - 192 * q^93 - 160 * q^94 - 96 * q^95 - 352 * q^96 - 216 * q^97 - 176 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2496))\)

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
2496.2.a	\(\chi_{2496}(1, \cdot)\)	2496.2.a.a	1	1
		2496.2.a.b	1
		2496.2.a.c	1
		2496.2.a.d	1
		2496.2.a.e	1
		2496.2.a.f	1
		2496.2.a.g	1
		2496.2.a.h	1
		2496.2.a.i	1
		2496.2.a.j	1
		2496.2.a.k	1
		2496.2.a.l	1
		2496.2.a.m	1
		2496.2.a.n	1
		2496.2.a.o	1
		2496.2.a.p	1
		2496.2.a.q	1
		2496.2.a.r	1
		2496.2.a.s	1
		2496.2.a.t	1
		2496.2.a.u	1
		2496.2.a.v	1
		2496.2.a.w	1
		2496.2.a.x	1
		2496.2.a.y	1
		2496.2.a.z	1
		2496.2.a.ba	1
		2496.2.a.bb	1
		2496.2.a.bc	1
		2496.2.a.bd	1
		2496.2.a.be	2
		2496.2.a.bf	2
		2496.2.a.bg	2
		2496.2.a.bh	2
		2496.2.a.bi	2
		2496.2.a.bj	2
		2496.2.a.bk	3
		2496.2.a.bl	3
2496.2.c	\(\chi_{2496}(961, \cdot)\)	2496.2.c.a	2	1
		2496.2.c.b	2
		2496.2.c.c	2
		2496.2.c.d	2
		2496.2.c.e	2
		2496.2.c.f	2
		2496.2.c.g	2
		2496.2.c.h	2
		2496.2.c.i	2
		2496.2.c.j	2
		2496.2.c.k	2
		2496.2.c.l	2
		2496.2.c.m	2
		2496.2.c.n	2
		2496.2.c.o	6
		2496.2.c.p	6
		2496.2.c.q	8
		2496.2.c.r	8
2496.2.d	\(\chi_{2496}(1535, \cdot)\)	2496.2.d.a	2	1
		2496.2.d.b	2
		2496.2.d.c	2
		2496.2.d.d	2
		2496.2.d.e	2
		2496.2.d.f	2
		2496.2.d.g	2
		2496.2.d.h	2
		2496.2.d.i	4
		2496.2.d.j	4
		2496.2.d.k	4
		2496.2.d.l	4
		2496.2.d.m	8
		2496.2.d.n	8
		2496.2.d.o	12
		2496.2.d.p	16
		2496.2.d.q	20
2496.2.g	\(\chi_{2496}(1249, \cdot)\)	2496.2.g.a	4	1
		2496.2.g.b	4
		2496.2.g.c	4
		2496.2.g.d	4
		2496.2.g.e	8
		2496.2.g.f	8
		2496.2.g.g	8
		2496.2.g.h	8
2496.2.h	\(\chi_{2496}(1247, \cdot)\)	n/a	112	1
2496.2.j	\(\chi_{2496}(287, \cdot)\)	2496.2.j.a	4	1
		2496.2.j.b	4
		2496.2.j.c	12
		2496.2.j.d	12
		2496.2.j.e	32
		2496.2.j.f	32
2496.2.m	\(\chi_{2496}(2209, \cdot)\)	2496.2.m.a	8	1
		2496.2.m.b	8
		2496.2.m.c	16
		2496.2.m.d	24
2496.2.n	\(\chi_{2496}(2495, \cdot)\)	n/a	108	1
2496.2.q	\(\chi_{2496}(1153, \cdot)\)	n/a	112	2
2496.2.r	\(\chi_{2496}(463, \cdot)\)	n/a	112	2
2496.2.u	\(\chi_{2496}(593, \cdot)\)	n/a	216	2
2496.2.v	\(\chi_{2496}(623, \cdot)\)	n/a	216	2
2496.2.x	\(\chi_{2496}(625, \cdot)\)	2496.2.x.a	40	2
		2496.2.x.b	56
2496.2.bb	\(\chi_{2496}(31, \cdot)\)	n/a	112	2
2496.2.bc	\(\chi_{2496}(1087, \cdot)\)	n/a	112	2
2496.2.bf	\(\chi_{2496}(1217, \cdot)\)	n/a	216	2
2496.2.bg	\(\chi_{2496}(161, \cdot)\)	n/a	224	2
2496.2.bh	\(\chi_{2496}(911, \cdot)\)	n/a	192	2
2496.2.bj	\(\chi_{2496}(337, \cdot)\)	n/a	112	2
2496.2.bm	\(\chi_{2496}(785, \cdot)\)	n/a	216	2
2496.2.bn	\(\chi_{2496}(655, \cdot)\)	n/a	112	2
2496.2.bq	\(\chi_{2496}(95, \cdot)\)	n/a	224	2
2496.2.br	\(\chi_{2496}(289, \cdot)\)	n/a	112	2
2496.2.bu	\(\chi_{2496}(191, \cdot)\)	n/a	216	2
2496.2.bv	\(\chi_{2496}(1921, \cdot)\)	n/a	112	2
2496.2.bz	\(\chi_{2496}(959, \cdot)\)	n/a	216	2
2496.2.ca	\(\chi_{2496}(673, \cdot)\)	n/a	112	2
2496.2.cd	\(\chi_{2496}(1439, \cdot)\)	n/a	224	2
2496.2.cf	\(\chi_{2496}(473, \cdot)\)	None	0	4
2496.2.ch	\(\chi_{2496}(343, \cdot)\)	None	0	4
2496.2.ci	\(\chi_{2496}(25, \cdot)\)	None	0	4
2496.2.ck	\(\chi_{2496}(313, \cdot)\)	None	0	4
2496.2.cn	\(\chi_{2496}(599, \cdot)\)	None	0	4
2496.2.cp	\(\chi_{2496}(311, \cdot)\)	None	0	4
2496.2.cq	\(\chi_{2496}(281, \cdot)\)	None	0	4
2496.2.cs	\(\chi_{2496}(151, \cdot)\)	None	0	4
2496.2.cu	\(\chi_{2496}(305, \cdot)\)	n/a	432	4
2496.2.cx	\(\chi_{2496}(175, \cdot)\)	n/a	224	4
2496.2.cz	\(\chi_{2496}(49, \cdot)\)	n/a	224	4
2496.2.db	\(\chi_{2496}(815, \cdot)\)	n/a	432	4
2496.2.dc	\(\chi_{2496}(353, \cdot)\)	n/a	448	4
2496.2.dd	\(\chi_{2496}(449, \cdot)\)	n/a	432	4
2496.2.dg	\(\chi_{2496}(319, \cdot)\)	n/a	224	4
2496.2.dh	\(\chi_{2496}(223, \cdot)\)	n/a	224	4
2496.2.dl	\(\chi_{2496}(529, \cdot)\)	n/a	224	4
2496.2.dn	\(\chi_{2496}(335, \cdot)\)	n/a	432	4
2496.2.dp	\(\chi_{2496}(847, \cdot)\)	n/a	224	4
2496.2.dq	\(\chi_{2496}(977, \cdot)\)	n/a	432	4
2496.2.ds	\(\chi_{2496}(157, \cdot)\)	n/a	1536	8
2496.2.dt	\(\chi_{2496}(155, \cdot)\)	n/a	3552	8
2496.2.dw	\(\chi_{2496}(5, \cdot)\)	n/a	3552	8
2496.2.dx	\(\chi_{2496}(187, \cdot)\)	n/a	1792	8
2496.2.ea	\(\chi_{2496}(317, \cdot)\)	n/a	3552	8
2496.2.eb	\(\chi_{2496}(499, \cdot)\)	n/a	1792	8
2496.2.ee	\(\chi_{2496}(131, \cdot)\)	n/a	3072	8
2496.2.ef	\(\chi_{2496}(181, \cdot)\)	n/a	1792	8
2496.2.ej	\(\chi_{2496}(487, \cdot)\)	None	0	8
2496.2.el	\(\chi_{2496}(41, \cdot)\)	None	0	8
2496.2.en	\(\chi_{2496}(263, \cdot)\)	None	0	8
2496.2.ep	\(\chi_{2496}(23, \cdot)\)	None	0	8
2496.2.eq	\(\chi_{2496}(121, \cdot)\)	None	0	8
2496.2.es	\(\chi_{2496}(217, \cdot)\)	None	0	8
2496.2.eu	\(\chi_{2496}(7, \cdot)\)	None	0	8
2496.2.ew	\(\chi_{2496}(137, \cdot)\)	None	0	8
2496.2.fa	\(\chi_{2496}(179, \cdot)\)	n/a	7104	16
2496.2.fb	\(\chi_{2496}(61, \cdot)\)	n/a	3584	16
2496.2.fe	\(\chi_{2496}(115, \cdot)\)	n/a	3584	16
2496.2.ff	\(\chi_{2496}(149, \cdot)\)	n/a	7104	16
2496.2.fi	\(\chi_{2496}(19, \cdot)\)	n/a	3584	16
2496.2.fj	\(\chi_{2496}(245, \cdot)\)	n/a	7104	16
2496.2.fm	\(\chi_{2496}(205, \cdot)\)	n/a	3584	16
2496.2.fn	\(\chi_{2496}(35, \cdot)\)	n/a	7104	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2496))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2496)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2496))\)\(^{\oplus 1}\)