Space of modular forms of level 1200 and weight 4

• Label: 1200.4
• Level: 1200
• Weight: 4
• Dimension: 44609
• Nonzero newspaces: 28
• Sturm bound: 307200
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(307200\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1200))\).

	Total	New	Old
Modular forms	116768	44977	71791
Cusp forms	113632	44609	69023
Eisenstein series	3136	368	2768

Trace form

44609 * q - 23 * q^3 - 72 * q^4 - 12 * q^6 - 12 * q^7 + 84 * q^8 + 47 * q^9 - 64 * q^10 - 60 * q^11 - 128 * q^12 - 442 * q^13 - 348 * q^14 - 36 * q^15 - 384 * q^16 + 390 * q^17 - 8 * q^18 + 916 * q^19 + 234 * q^21 + 616 * q^22 + 88 * q^23 + 84 * q^24 - 192 * q^25 - 20 * q^26 - 1067 * q^27 + 1360 * q^28 + 1194 * q^29 + 1600 * q^30 + 276 * q^31 + 1760 * q^32 + 590 * q^33 - 2536 * q^34 - 456 * q^35 - 1400 * q^36 - 4226 * q^37 - 7032 * q^38 - 284 * q^39 - 6304 * q^40 - 4322 * q^41 - 3948 * q^42 - 1364 * q^43 - 4456 * q^44 + 66 * q^45 - 80 * q^46 + 240 * q^47 + 4872 * q^48 + 5009 * q^49 + 5680 * q^50 + 1470 * q^51 + 16256 * q^52 + 5810 * q^53 + 1676 * q^54 + 452 * q^55 + 1344 * q^56 - 1226 * q^57 + 1464 * q^58 - 628 * q^59 - 544 * q^60 - 786 * q^61 - 996 * q^62 + 3242 * q^63 - 17616 * q^64 + 1048 * q^65 - 15260 * q^66 + 13772 * q^67 - 13440 * q^68 - 1254 * q^69 - 1648 * q^70 - 3528 * q^71 + 1180 * q^72 - 4242 * q^73 + 14508 * q^74 - 6112 * q^75 + 14544 * q^76 - 4336 * q^77 + 20016 * q^78 - 25628 * q^79 + 12640 * q^80 - 2189 * q^81 + 24296 * q^82 - 8476 * q^83 + 17616 * q^84 + 15328 * q^85 + 7760 * q^86 + 28 * q^87 + 7344 * q^88 + 814 * q^89 - 3752 * q^90 + 11444 * q^91 - 16880 * q^92 - 3482 * q^93 - 18504 * q^94 + 4152 * q^95 - 13856 * q^96 - 14994 * q^97 - 18488 * q^98 + 12296 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1200))\)

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
1200.4.a	\(\chi_{1200}(1, \cdot)\)	1200.4.a.a	1	1
		1200.4.a.b	1
		1200.4.a.c	1
		1200.4.a.d	1
		1200.4.a.e	1
		1200.4.a.f	1
		1200.4.a.g	1
		1200.4.a.h	1
		1200.4.a.i	1
		1200.4.a.j	1
		1200.4.a.k	1
		1200.4.a.l	1
		1200.4.a.m	1
		1200.4.a.n	1
		1200.4.a.o	1
		1200.4.a.p	1
		1200.4.a.q	1
		1200.4.a.r	1
		1200.4.a.s	1
		1200.4.a.t	1
		1200.4.a.u	1
		1200.4.a.v	1
		1200.4.a.w	1
		1200.4.a.x	1
		1200.4.a.y	1
		1200.4.a.z	1
		1200.4.a.ba	1
		1200.4.a.bb	1
		1200.4.a.bc	1
		1200.4.a.bd	1
		1200.4.a.be	1
		1200.4.a.bf	1
		1200.4.a.bg	1
		1200.4.a.bh	1
		1200.4.a.bi	1
		1200.4.a.bj	1
		1200.4.a.bk	1
		1200.4.a.bl	2
		1200.4.a.bm	2
		1200.4.a.bn	2
		1200.4.a.bo	2
		1200.4.a.bp	2
		1200.4.a.bq	2
		1200.4.a.br	2
		1200.4.a.bs	2
		1200.4.a.bt	2
		1200.4.a.bu	2
1200.4.b	\(\chi_{1200}(551, \cdot)\)	None	0	1
1200.4.d	\(\chi_{1200}(649, \cdot)\)	None	0	1
1200.4.f	\(\chi_{1200}(49, \cdot)\)	1200.4.f.a	2	1
		1200.4.f.b	2
		1200.4.f.c	2
		1200.4.f.d	2
		1200.4.f.e	2
		1200.4.f.f	2
		1200.4.f.g	2
		1200.4.f.h	2
		1200.4.f.i	2
		1200.4.f.j	2
		1200.4.f.k	2
		1200.4.f.l	2
		1200.4.f.m	2
		1200.4.f.n	2
		1200.4.f.o	2
		1200.4.f.p	2
		1200.4.f.q	2
		1200.4.f.r	2
		1200.4.f.s	2
		1200.4.f.t	2
		1200.4.f.u	2
		1200.4.f.v	4
		1200.4.f.w	4
		1200.4.f.x	4
1200.4.h	\(\chi_{1200}(1151, \cdot)\)	n/a	114	1
1200.4.k	\(\chi_{1200}(601, \cdot)\)	None	0	1
1200.4.m	\(\chi_{1200}(599, \cdot)\)	None	0	1
1200.4.o	\(\chi_{1200}(1199, \cdot)\)	n/a	108	1
1200.4.s	\(\chi_{1200}(301, \cdot)\)	n/a	456	2
1200.4.t	\(\chi_{1200}(299, \cdot)\)	n/a	856	2
1200.4.v	\(\chi_{1200}(257, \cdot)\)	n/a	212	2
1200.4.w	\(\chi_{1200}(607, \cdot)\)	n/a	108	2
1200.4.y	\(\chi_{1200}(643, \cdot)\)	n/a	432	2
1200.4.bb	\(\chi_{1200}(893, \cdot)\)	n/a	856	2
1200.4.bc	\(\chi_{1200}(43, \cdot)\)	n/a	432	2
1200.4.bf	\(\chi_{1200}(293, \cdot)\)	n/a	856	2
1200.4.bh	\(\chi_{1200}(7, \cdot)\)	None	0	2
1200.4.bi	\(\chi_{1200}(857, \cdot)\)	None	0	2
1200.4.bk	\(\chi_{1200}(251, \cdot)\)	n/a	900	2
1200.4.bl	\(\chi_{1200}(349, \cdot)\)	n/a	432	2
1200.4.bo	\(\chi_{1200}(241, \cdot)\)	n/a	360	4
1200.4.bq	\(\chi_{1200}(191, \cdot)\)	n/a	720	4
1200.4.bs	\(\chi_{1200}(289, \cdot)\)	n/a	360	4
1200.4.bu	\(\chi_{1200}(169, \cdot)\)	None	0	4
1200.4.bw	\(\chi_{1200}(71, \cdot)\)	None	0	4
1200.4.by	\(\chi_{1200}(239, \cdot)\)	n/a	720	4
1200.4.ca	\(\chi_{1200}(119, \cdot)\)	None	0	4
1200.4.cc	\(\chi_{1200}(121, \cdot)\)	None	0	4
1200.4.ce	\(\chi_{1200}(59, \cdot)\)	n/a	5728	8
1200.4.cf	\(\chi_{1200}(61, \cdot)\)	n/a	2880	8
1200.4.cj	\(\chi_{1200}(137, \cdot)\)	None	0	8
1200.4.ck	\(\chi_{1200}(103, \cdot)\)	None	0	8
1200.4.cm	\(\chi_{1200}(53, \cdot)\)	n/a	5728	8
1200.4.cp	\(\chi_{1200}(67, \cdot)\)	n/a	2880	8
1200.4.cq	\(\chi_{1200}(173, \cdot)\)	n/a	5728	8
1200.4.ct	\(\chi_{1200}(163, \cdot)\)	n/a	2880	8
1200.4.cv	\(\chi_{1200}(127, \cdot)\)	n/a	720	8
1200.4.cw	\(\chi_{1200}(17, \cdot)\)	n/a	1424	8
1200.4.da	\(\chi_{1200}(109, \cdot)\)	n/a	2880	8
1200.4.db	\(\chi_{1200}(11, \cdot)\)	n/a	5728	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1200))\) into lower level spaces

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