Space of modular forms of level 2400 and weight 2

• Label: 2400.2
• Level: 2400
• Weight: 2
• Dimension: 59314
• Nonzero newspaces: 40
• Sturm bound: 614400
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(614400\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2400))\).

	Total	New	Old
Modular forms	157184	60134	97050
Cusp forms	150017	59314	90703
Eisenstein series	7167	820	6347

Trace form

59314 * q - 38 * q^3 - 104 * q^4 - 84 * q^6 - 76 * q^7 - 74 * q^9 - 128 * q^10 - 68 * q^12 - 116 * q^13 - 32 * q^14 - 48 * q^15 - 208 * q^16 - 16 * q^17 - 60 * q^18 - 100 * q^19 - 100 * q^21 - 128 * q^22 - 24 * q^23 - 40 * q^24 - 192 * q^25 + 40 * q^26 - 74 * q^27 - 64 * q^28 - 28 * q^29 - 64 * q^30 - 236 * q^31 + 40 * q^32 - 192 * q^33 - 80 * q^34 - 48 * q^35 - 32 * q^36 - 244 * q^37 + 40 * q^38 - 112 * q^39 - 128 * q^40 - 120 * q^41 + 8 * q^42 - 204 * q^43 + 8 * q^44 - 80 * q^45 - 168 * q^46 - 72 * q^47 - 138 * q^49 - 136 * q^51 - 56 * q^52 - 44 * q^53 - 136 * q^55 + 56 * q^56 - 8 * q^57 - 32 * q^58 + 64 * q^59 - 228 * q^61 + 48 * q^62 + 32 * q^63 + 160 * q^64 + 64 * q^65 + 196 * q^66 + 68 * q^67 + 440 * q^68 + 76 * q^69 + 160 * q^70 + 168 * q^71 + 368 * q^72 + 60 * q^73 + 672 * q^74 + 8 * q^75 + 184 * q^76 + 320 * q^77 + 492 * q^78 + 164 * q^79 + 320 * q^80 + 178 * q^81 + 456 * q^82 + 160 * q^83 + 424 * q^84 + 64 * q^85 + 448 * q^86 + 164 * q^87 + 512 * q^88 + 256 * q^89 + 176 * q^90 + 496 * q^92 + 152 * q^93 + 256 * q^94 + 48 * q^95 + 32 * q^96 - 140 * q^97 + 112 * q^98 + 196 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2400))\)

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
2400.2.a	\(\chi_{2400}(1, \cdot)\)	2400.2.a.a	1	1
		2400.2.a.b	1
		2400.2.a.c	1
		2400.2.a.d	1
		2400.2.a.e	1
		2400.2.a.f	1
		2400.2.a.g	1
		2400.2.a.h	1
		2400.2.a.i	1
		2400.2.a.j	1
		2400.2.a.k	1
		2400.2.a.l	1
		2400.2.a.m	1
		2400.2.a.n	1
		2400.2.a.o	1
		2400.2.a.p	1
		2400.2.a.q	1
		2400.2.a.r	1
		2400.2.a.s	1
		2400.2.a.t	1
		2400.2.a.u	1
		2400.2.a.v	1
		2400.2.a.w	1
		2400.2.a.x	1
		2400.2.a.y	1
		2400.2.a.z	1
		2400.2.a.ba	1
		2400.2.a.bb	1
		2400.2.a.bc	1
		2400.2.a.bd	1
		2400.2.a.be	1
		2400.2.a.bf	1
		2400.2.a.bg	1
		2400.2.a.bh	1
		2400.2.a.bi	2
		2400.2.a.bj	2
2400.2.b	\(\chi_{2400}(2351, \cdot)\)	2400.2.b.a	2	1
		2400.2.b.b	4
		2400.2.b.c	4
		2400.2.b.d	4
		2400.2.b.e	8
		2400.2.b.f	8
		2400.2.b.g	12
		2400.2.b.h	12
		2400.2.b.i	16
2400.2.d	\(\chi_{2400}(49, \cdot)\)	2400.2.d.a	2	1
		2400.2.d.b	2
		2400.2.d.c	2
		2400.2.d.d	2
		2400.2.d.e	6
		2400.2.d.f	6
		2400.2.d.g	8
		2400.2.d.h	8
2400.2.f	\(\chi_{2400}(1249, \cdot)\)	2400.2.f.a	2	1
		2400.2.f.b	2
		2400.2.f.c	2
		2400.2.f.d	2
		2400.2.f.e	2
		2400.2.f.f	2
		2400.2.f.g	2
		2400.2.f.h	2
		2400.2.f.i	2
		2400.2.f.j	2
		2400.2.f.k	2
		2400.2.f.l	2
		2400.2.f.m	2
		2400.2.f.n	2
		2400.2.f.o	2
		2400.2.f.p	2
		2400.2.f.q	2
		2400.2.f.r	2
2400.2.h	\(\chi_{2400}(1151, \cdot)\)	2400.2.h.a	4	1
		2400.2.h.b	4
		2400.2.h.c	4
		2400.2.h.d	4
		2400.2.h.e	4
		2400.2.h.f	16
		2400.2.h.g	16
		2400.2.h.h	24
2400.2.k	\(\chi_{2400}(1201, \cdot)\)	2400.2.k.a	2	1
		2400.2.k.b	2
		2400.2.k.c	6
		2400.2.k.d	8
		2400.2.k.e	8
		2400.2.k.f	12
2400.2.m	\(\chi_{2400}(1199, \cdot)\)	2400.2.m.a	4	1
		2400.2.m.b	8
		2400.2.m.c	16
		2400.2.m.d	16
		2400.2.m.e	24
2400.2.o	\(\chi_{2400}(2399, \cdot)\)	2400.2.o.a	4	1
		2400.2.o.b	4
		2400.2.o.c	4
		2400.2.o.d	4
		2400.2.o.e	4
		2400.2.o.f	4
		2400.2.o.g	4
		2400.2.o.h	4
		2400.2.o.i	4
		2400.2.o.j	4
		2400.2.o.k	16
		2400.2.o.l	16
2400.2.s	\(\chi_{2400}(601, \cdot)\)	None	0	2
2400.2.t	\(\chi_{2400}(599, \cdot)\)	None	0	2
2400.2.v	\(\chi_{2400}(257, \cdot)\)	n/a	144	2
2400.2.w	\(\chi_{2400}(607, \cdot)\)	2400.2.w.a	4	2
		2400.2.w.b	4
		2400.2.w.c	4
		2400.2.w.d	4
		2400.2.w.e	4
		2400.2.w.f	4
		2400.2.w.g	8
		2400.2.w.h	8
		2400.2.w.i	8
		2400.2.w.j	8
		2400.2.w.k	8
		2400.2.w.l	8
2400.2.y	\(\chi_{2400}(7, \cdot)\)	None	0	2
2400.2.bb	\(\chi_{2400}(857, \cdot)\)	None	0	2
2400.2.bc	\(\chi_{2400}(1207, \cdot)\)	None	0	2
2400.2.bf	\(\chi_{2400}(2057, \cdot)\)	None	0	2
2400.2.bh	\(\chi_{2400}(943, \cdot)\)	2400.2.bh.a	16	2
		2400.2.bh.b	24
		2400.2.bh.c	32
2400.2.bi	\(\chi_{2400}(593, \cdot)\)	n/a	136	2
2400.2.bk	\(\chi_{2400}(551, \cdot)\)	None	0	2
2400.2.bl	\(\chi_{2400}(649, \cdot)\)	None	0	2
2400.2.bo	\(\chi_{2400}(481, \cdot)\)	n/a	240	4
2400.2.bp	\(\chi_{2400}(43, \cdot)\)	n/a	576	4
2400.2.bs	\(\chi_{2400}(893, \cdot)\)	n/a	1136	4
2400.2.bt	\(\chi_{2400}(299, \cdot)\)	n/a	1136	4
2400.2.bw	\(\chi_{2400}(301, \cdot)\)	n/a	608	4
2400.2.by	\(\chi_{2400}(251, \cdot)\)	n/a	1192	4
2400.2.bz	\(\chi_{2400}(349, \cdot)\)	n/a	576	4
2400.2.cc	\(\chi_{2400}(293, \cdot)\)	n/a	1136	4
2400.2.cd	\(\chi_{2400}(643, \cdot)\)	n/a	576	4
2400.2.cg	\(\chi_{2400}(191, \cdot)\)	n/a	480	4
2400.2.ci	\(\chi_{2400}(289, \cdot)\)	n/a	240	4
2400.2.ck	\(\chi_{2400}(529, \cdot)\)	n/a	240	4
2400.2.cm	\(\chi_{2400}(431, \cdot)\)	n/a	464	4
2400.2.co	\(\chi_{2400}(479, \cdot)\)	n/a	480	4
2400.2.cq	\(\chi_{2400}(239, \cdot)\)	n/a	464	4
2400.2.cs	\(\chi_{2400}(241, \cdot)\)	n/a	240	4
2400.2.cu	\(\chi_{2400}(119, \cdot)\)	None	0	8
2400.2.cv	\(\chi_{2400}(121, \cdot)\)	None	0	8
2400.2.cz	\(\chi_{2400}(17, \cdot)\)	n/a	928	8
2400.2.da	\(\chi_{2400}(367, \cdot)\)	n/a	480	8
2400.2.dc	\(\chi_{2400}(137, \cdot)\)	None	0	8
2400.2.df	\(\chi_{2400}(103, \cdot)\)	None	0	8
2400.2.dg	\(\chi_{2400}(233, \cdot)\)	None	0	8
2400.2.dj	\(\chi_{2400}(487, \cdot)\)	None	0	8
2400.2.dl	\(\chi_{2400}(127, \cdot)\)	n/a	480	8
2400.2.dm	\(\chi_{2400}(353, \cdot)\)	n/a	960	8
2400.2.dq	\(\chi_{2400}(169, \cdot)\)	None	0	8
2400.2.dr	\(\chi_{2400}(71, \cdot)\)	None	0	8
2400.2.ds	\(\chi_{2400}(173, \cdot)\)	n/a	7616	16
2400.2.dv	\(\chi_{2400}(67, \cdot)\)	n/a	3840	16
2400.2.dx	\(\chi_{2400}(109, \cdot)\)	n/a	3840	16
2400.2.dy	\(\chi_{2400}(11, \cdot)\)	n/a	7616	16
2400.2.ea	\(\chi_{2400}(61, \cdot)\)	n/a	3840	16
2400.2.ed	\(\chi_{2400}(59, \cdot)\)	n/a	7616	16
2400.2.ef	\(\chi_{2400}(163, \cdot)\)	n/a	3840	16
2400.2.eg	\(\chi_{2400}(53, \cdot)\)	n/a	7616	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)