Space of modular forms of level 2548 and weight 2

• Label: 2548.2
• Level: 2548
• Weight: 2
• Dimension: 108209
• Nonzero newspaces: 60
• Sturm bound: 790272
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(790272\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2548))\).

	Total	New	Old
Modular forms	201168	110345	90823
Cusp forms	193969	108209	85760
Eisenstein series	7199	2136	5063

Trace form

108209 * q - 156 * q^2 - 4 * q^3 - 156 * q^4 - 324 * q^5 - 144 * q^6 - 8 * q^7 - 264 * q^8 - 312 * q^9 - 120 * q^10 + 6 * q^11 - 90 * q^12 - 334 * q^13 - 372 * q^14 + 12 * q^15 - 108 * q^16 - 327 * q^17 - 114 * q^18 + 8 * q^19 - 120 * q^20 - 338 * q^21 - 294 * q^22 - 144 * q^24 - 253 * q^25 - 159 * q^26 - 4 * q^27 - 228 * q^28 - 501 * q^29 - 120 * q^30 + 26 * q^31 - 126 * q^32 - 246 * q^33 - 120 * q^34 + 30 * q^35 - 216 * q^36 - 215 * q^37 - 66 * q^38 + 25 * q^39 - 306 * q^40 - 147 * q^41 - 150 * q^42 + 54 * q^43 - 102 * q^44 - 39 * q^45 - 156 * q^46 + 114 * q^47 - 234 * q^48 - 212 * q^49 - 492 * q^50 + 156 * q^51 - 219 * q^52 - 636 * q^53 - 258 * q^54 + 144 * q^55 - 156 * q^56 - 526 * q^57 - 216 * q^58 + 42 * q^59 - 222 * q^60 - 225 * q^61 - 156 * q^62 + 36 * q^63 - 210 * q^64 - 273 * q^65 - 318 * q^66 + 32 * q^67 - 66 * q^68 - 270 * q^69 - 162 * q^70 + 36 * q^71 - 126 * q^72 - 112 * q^73 - 108 * q^74 + 168 * q^75 - 84 * q^76 - 198 * q^77 - 237 * q^78 + 328 * q^79 - 252 * q^80 + 42 * q^81 - 246 * q^82 + 186 * q^83 - 636 * q^84 - 111 * q^85 - 456 * q^86 + 132 * q^87 - 492 * q^88 - 12 * q^89 - 1008 * q^90 + 64 * q^91 - 876 * q^92 - 442 * q^93 - 654 * q^94 - 36 * q^95 - 1044 * q^96 - 244 * q^97 - 792 * q^98 + 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2548))\)

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
2548.2.a	\(\chi_{2548}(1, \cdot)\)	2548.2.a.a	1	1
		2548.2.a.b	1
		2548.2.a.c	1
		2548.2.a.d	1
		2548.2.a.e	1
		2548.2.a.f	1
		2548.2.a.g	1
		2548.2.a.h	1
		2548.2.a.i	1
		2548.2.a.j	1
		2548.2.a.k	1
		2548.2.a.l	2
		2548.2.a.m	2
		2548.2.a.n	3
		2548.2.a.o	3
		2548.2.a.p	4
		2548.2.a.q	4
		2548.2.a.r	6
		2548.2.a.s	6
2548.2.f	\(\chi_{2548}(391, \cdot)\)	n/a	240	1
2548.2.g	\(\chi_{2548}(2157, \cdot)\)	2548.2.g.a	4	1
		2548.2.g.b	4
		2548.2.g.c	4
		2548.2.g.d	4
		2548.2.g.e	6
		2548.2.g.f	6
		2548.2.g.g	8
		2548.2.g.h	12
2548.2.h	\(\chi_{2548}(2547, \cdot)\)	n/a	272	1
2548.2.i	\(\chi_{2548}(165, \cdot)\)	2548.2.i.a	2	2
		2548.2.i.b	2
		2548.2.i.c	2
		2548.2.i.d	2
		2548.2.i.e	2
		2548.2.i.f	2
		2548.2.i.g	2
		2548.2.i.h	2
		2548.2.i.i	4
		2548.2.i.j	4
		2548.2.i.k	4
		2548.2.i.l	4
		2548.2.i.m	12
		2548.2.i.n	18
		2548.2.i.o	32
2548.2.j	\(\chi_{2548}(1145, \cdot)\)	2548.2.j.a	2	2
		2548.2.j.b	2
		2548.2.j.c	2
		2548.2.j.d	2
		2548.2.j.e	2
		2548.2.j.f	2
		2548.2.j.g	2
		2548.2.j.h	2
		2548.2.j.i	2
		2548.2.j.j	2
		2548.2.j.k	4
		2548.2.j.l	4
		2548.2.j.m	4
		2548.2.j.n	4
		2548.2.j.o	6
		2548.2.j.p	6
		2548.2.j.q	8
		2548.2.j.r	12
		2548.2.j.s	12
2548.2.k	\(\chi_{2548}(393, \cdot)\)	2548.2.k.a	2	2
		2548.2.k.b	2
		2548.2.k.c	2
		2548.2.k.d	2
		2548.2.k.e	4
		2548.2.k.f	4
		2548.2.k.g	12
		2548.2.k.h	18
		2548.2.k.i	18
		2548.2.k.j	32
2548.2.l	\(\chi_{2548}(373, \cdot)\)	2548.2.l.a	2	2
		2548.2.l.b	2
		2548.2.l.c	2
		2548.2.l.d	2
		2548.2.l.e	2
		2548.2.l.f	2
		2548.2.l.g	2
		2548.2.l.h	2
		2548.2.l.i	4
		2548.2.l.j	4
		2548.2.l.k	4
		2548.2.l.l	4
		2548.2.l.m	12
		2548.2.l.n	18
		2548.2.l.o	32
2548.2.m	\(\chi_{2548}(99, \cdot)\)	n/a	554	2
2548.2.n	\(\chi_{2548}(489, \cdot)\)	2548.2.n.a	40	2
		2548.2.n.b	56
2548.2.u	\(\chi_{2548}(589, \cdot)\)	2548.2.u.a	2	2
		2548.2.u.b	16
		2548.2.u.c	16
		2548.2.u.d	18
		2548.2.u.e	18
		2548.2.u.f	24
2548.2.v	\(\chi_{2548}(783, \cdot)\)	n/a	544	2
2548.2.w	\(\chi_{2548}(803, \cdot)\)	n/a	544	2
2548.2.x	\(\chi_{2548}(1195, \cdot)\)	n/a	544	2
2548.2.y	\(\chi_{2548}(753, \cdot)\)	2548.2.y.a	8	2
		2548.2.y.b	8
		2548.2.y.c	8
		2548.2.y.d	12
		2548.2.y.e	16
		2548.2.y.f	16
		2548.2.y.g	24
2548.2.z	\(\chi_{2548}(1587, \cdot)\)	n/a	480	2
2548.2.ba	\(\chi_{2548}(815, \cdot)\)	n/a	544	2
2548.2.bb	\(\chi_{2548}(569, \cdot)\)	2548.2.bb.a	2	2
		2548.2.bb.b	2
		2548.2.bb.c	16
		2548.2.bb.d	16
		2548.2.bb.e	16
		2548.2.bb.f	18
		2548.2.bb.g	24
2548.2.bc	\(\chi_{2548}(979, \cdot)\)	n/a	544	2
2548.2.bp	\(\chi_{2548}(1011, \cdot)\)	n/a	544	2
2548.2.bq	\(\chi_{2548}(361, \cdot)\)	2548.2.bq.a	2	2
		2548.2.bq.b	2
		2548.2.bq.c	16
		2548.2.bq.d	16
		2548.2.bq.e	16
		2548.2.bq.f	18
		2548.2.bq.g	24
2548.2.br	\(\chi_{2548}(607, \cdot)\)	n/a	544	2
2548.2.bs	\(\chi_{2548}(365, \cdot)\)	n/a	336	6
2548.2.bt	\(\chi_{2548}(717, \cdot)\)	n/a	188	4
2548.2.bu	\(\chi_{2548}(67, \cdot)\)	n/a	1088	4
2548.2.cb	\(\chi_{2548}(275, \cdot)\)	n/a	1088	4
2548.2.cc	\(\chi_{2548}(97, \cdot)\)	n/a	184	4
2548.2.cd	\(\chi_{2548}(1097, \cdot)\)	n/a	184	4
2548.2.ce	\(\chi_{2548}(687, \cdot)\)	n/a	1108	4
2548.2.cf	\(\chi_{2548}(655, \cdot)\)	n/a	1088	4
2548.2.cg	\(\chi_{2548}(509, \cdot)\)	n/a	188	4
2548.2.cj	\(\chi_{2548}(363, \cdot)\)	n/a	2328	6
2548.2.ck	\(\chi_{2548}(337, \cdot)\)	n/a	384	6
2548.2.cl	\(\chi_{2548}(27, \cdot)\)	n/a	2016	6
2548.2.cq	\(\chi_{2548}(9, \cdot)\)	n/a	780	12
2548.2.cr	\(\chi_{2548}(29, \cdot)\)	n/a	792	12
2548.2.cs	\(\chi_{2548}(53, \cdot)\)	n/a	672	12
2548.2.ct	\(\chi_{2548}(289, \cdot)\)	n/a	780	12
2548.2.cw	\(\chi_{2548}(125, \cdot)\)	n/a	768	12
2548.2.cx	\(\chi_{2548}(239, \cdot)\)	n/a	4656	12
2548.2.cy	\(\chi_{2548}(3, \cdot)\)	n/a	4656	12
2548.2.cz	\(\chi_{2548}(121, \cdot)\)	n/a	780	12
2548.2.da	\(\chi_{2548}(283, \cdot)\)	n/a	4656	12
2548.2.dn	\(\chi_{2548}(251, \cdot)\)	n/a	4656	12
2548.2.do	\(\chi_{2548}(205, \cdot)\)	n/a	780	12
2548.2.dp	\(\chi_{2548}(87, \cdot)\)	n/a	4656	12
2548.2.dq	\(\chi_{2548}(131, \cdot)\)	n/a	4032	12
2548.2.dr	\(\chi_{2548}(25, \cdot)\)	n/a	792	12
2548.2.ds	\(\chi_{2548}(103, \cdot)\)	n/a	4656	12
2548.2.dt	\(\chi_{2548}(75, \cdot)\)	n/a	4656	12
2548.2.du	\(\chi_{2548}(55, \cdot)\)	n/a	4656	12
2548.2.dv	\(\chi_{2548}(225, \cdot)\)	n/a	792	12
2548.2.ec	\(\chi_{2548}(45, \cdot)\)	n/a	1560	24
2548.2.ed	\(\chi_{2548}(135, \cdot)\)	n/a	9312	24
2548.2.ee	\(\chi_{2548}(15, \cdot)\)	n/a	9312	24
2548.2.ef	\(\chi_{2548}(5, \cdot)\)	n/a	1584	24
2548.2.eg	\(\chi_{2548}(41, \cdot)\)	n/a	1584	24
2548.2.eh	\(\chi_{2548}(123, \cdot)\)	n/a	9312	24
2548.2.eo	\(\chi_{2548}(11, \cdot)\)	n/a	9312	24
2548.2.ep	\(\chi_{2548}(33, \cdot)\)	n/a	1560	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2548))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2548)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1274))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2548))\)\(^{\oplus 1}\)