Space of modular forms of level 1200 and weight 3

• Label: 1200.3
• Level: 1200
• Weight: 3
• Dimension: 29677
• Nonzero newspaces: 28
• Sturm bound: 230400
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(230400\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1200))\).

	Total	New	Old
Modular forms	78368	30047	48321
Cusp forms	75232	29677	45555
Eisenstein series	3136	370	2766

Trace form

29677 * q - 19 * q^3 - 40 * q^4 - 36 * q^6 - 26 * q^7 - 12 * q^8 - 13 * q^9 - 64 * q^10 + 32 * q^11 - 80 * q^12 + 2 * q^13 - 44 * q^14 + 24 * q^15 - 64 * q^16 + 52 * q^17 - 72 * q^18 - 142 * q^19 - 140 * q^21 + 24 * q^22 - 320 * q^23 - 44 * q^24 - 112 * q^25 - 100 * q^26 - 187 * q^27 - 560 * q^28 - 388 * q^29 - 320 * q^30 - 234 * q^31 - 960 * q^32 - 374 * q^33 - 1096 * q^34 - 96 * q^35 + 72 * q^36 - 414 * q^37 - 56 * q^38 - 124 * q^39 + 96 * q^40 + 148 * q^41 + 676 * q^42 + 170 * q^43 + 1208 * q^44 + 6 * q^45 + 1648 * q^46 + 384 * q^47 + 1096 * q^48 + 1167 * q^49 + 880 * q^50 - 124 * q^51 + 1248 * q^52 + 252 * q^53 - 188 * q^54 + 52 * q^55 - 224 * q^56 - 148 * q^57 - 472 * q^58 - 128 * q^59 + 96 * q^60 - 406 * q^61 - 276 * q^62 - 620 * q^63 + 752 * q^64 - 112 * q^65 + 1124 * q^66 - 2598 * q^67 + 2016 * q^68 - 14 * q^69 + 1232 * q^70 - 2048 * q^71 + 1404 * q^72 + 366 * q^73 + 2108 * q^74 - 392 * q^75 + 1456 * q^76 + 320 * q^77 + 976 * q^78 + 358 * q^79 - 160 * q^80 - 41 * q^81 - 184 * q^82 + 288 * q^83 - 592 * q^84 - 2032 * q^85 - 1264 * q^86 + 1298 * q^87 - 2384 * q^88 - 892 * q^89 - 1352 * q^90 + 3368 * q^91 - 3248 * q^92 + 56 * q^93 - 3432 * q^94 + 1152 * q^95 - 2208 * q^96 - 330 * q^97 - 2264 * q^98 + 1672 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1200))\)

We only show spaces with odd 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
1200.3.c	\(\chi_{1200}(449, \cdot)\)	1200.3.c.a	2	1
		1200.3.c.b	2
		1200.3.c.c	2
		1200.3.c.d	4
		1200.3.c.e	4
		1200.3.c.f	4
		1200.3.c.g	4
		1200.3.c.h	4
		1200.3.c.i	4
		1200.3.c.j	4
		1200.3.c.k	8
		1200.3.c.l	12
		1200.3.c.m	16
1200.3.e	\(\chi_{1200}(751, \cdot)\)	1200.3.e.a	2	1
		1200.3.e.b	2
		1200.3.e.c	2
		1200.3.e.d	2
		1200.3.e.e	2
		1200.3.e.f	2
		1200.3.e.g	2
		1200.3.e.h	2
		1200.3.e.i	2
		1200.3.e.j	4
		1200.3.e.k	4
		1200.3.e.l	4
		1200.3.e.m	4
		1200.3.e.n	4
1200.3.g	\(\chi_{1200}(151, \cdot)\)	None	0	1
1200.3.i	\(\chi_{1200}(1049, \cdot)\)	None	0	1
1200.3.j	\(\chi_{1200}(799, \cdot)\)	1200.3.j.a	4	1
		1200.3.j.b	4
		1200.3.j.c	4
		1200.3.j.d	8
		1200.3.j.e	8
		1200.3.j.f	8
1200.3.l	\(\chi_{1200}(401, \cdot)\)	1200.3.l.a	1	1
		1200.3.l.b	1
		1200.3.l.c	1
		1200.3.l.d	1
		1200.3.l.e	1
		1200.3.l.f	2
		1200.3.l.g	2
		1200.3.l.h	2
		1200.3.l.i	2
		1200.3.l.j	2
		1200.3.l.k	2
		1200.3.l.l	2
		1200.3.l.m	2
		1200.3.l.n	2
		1200.3.l.o	2
		1200.3.l.p	2
		1200.3.l.q	2
		1200.3.l.r	2
		1200.3.l.s	2
		1200.3.l.t	4
		1200.3.l.u	4
		1200.3.l.v	6
		1200.3.l.w	6
		1200.3.l.x	8
		1200.3.l.y	12
1200.3.n	\(\chi_{1200}(1001, \cdot)\)	None	0	1
1200.3.p	\(\chi_{1200}(199, \cdot)\)	None	0	1
1200.3.q	\(\chi_{1200}(499, \cdot)\)	n/a	288	2
1200.3.r	\(\chi_{1200}(101, \cdot)\)	n/a	596	2
1200.3.u	\(\chi_{1200}(407, \cdot)\)	None	0	2
1200.3.x	\(\chi_{1200}(457, \cdot)\)	None	0	2
1200.3.z	\(\chi_{1200}(107, \cdot)\)	n/a	568	2
1200.3.ba	\(\chi_{1200}(493, \cdot)\)	n/a	288	2
1200.3.bd	\(\chi_{1200}(443, \cdot)\)	n/a	568	2
1200.3.be	\(\chi_{1200}(157, \cdot)\)	n/a	288	2
1200.3.bg	\(\chi_{1200}(193, \cdot)\)	1200.3.bg.a	4	2
		1200.3.bg.b	4
		1200.3.bg.c	4
		1200.3.bg.d	4
		1200.3.bg.e	4
		1200.3.bg.f	4
		1200.3.bg.g	4
		1200.3.bg.h	4
		1200.3.bg.i	4
		1200.3.bg.j	4
		1200.3.bg.k	4
		1200.3.bg.l	4
		1200.3.bg.m	4
		1200.3.bg.n	4
		1200.3.bg.o	4
		1200.3.bg.p	4
		1200.3.bg.q	8
1200.3.bj	\(\chi_{1200}(143, \cdot)\)	n/a	144	2
1200.3.bm	\(\chi_{1200}(149, \cdot)\)	n/a	568	2
1200.3.bn	\(\chi_{1200}(451, \cdot)\)	n/a	304	2
1200.3.bp	\(\chi_{1200}(89, \cdot)\)	None	0	4
1200.3.br	\(\chi_{1200}(391, \cdot)\)	None	0	4
1200.3.bt	\(\chi_{1200}(31, \cdot)\)	n/a	240	4
1200.3.bv	\(\chi_{1200}(209, \cdot)\)	n/a	472	4
1200.3.bx	\(\chi_{1200}(439, \cdot)\)	None	0	4
1200.3.bz	\(\chi_{1200}(41, \cdot)\)	None	0	4
1200.3.cb	\(\chi_{1200}(161, \cdot)\)	n/a	472	4
1200.3.cd	\(\chi_{1200}(79, \cdot)\)	n/a	240	4
1200.3.cg	\(\chi_{1200}(221, \cdot)\)	n/a	3808	8
1200.3.ch	\(\chi_{1200}(19, \cdot)\)	n/a	1920	8
1200.3.ci	\(\chi_{1200}(47, \cdot)\)	n/a	960	8
1200.3.cl	\(\chi_{1200}(97, \cdot)\)	n/a	480	8
1200.3.cn	\(\chi_{1200}(133, \cdot)\)	n/a	1920	8
1200.3.co	\(\chi_{1200}(203, \cdot)\)	n/a	3808	8
1200.3.cr	\(\chi_{1200}(13, \cdot)\)	n/a	1920	8
1200.3.cs	\(\chi_{1200}(83, \cdot)\)	n/a	3808	8
1200.3.cu	\(\chi_{1200}(73, \cdot)\)	None	0	8
1200.3.cx	\(\chi_{1200}(23, \cdot)\)	None	0	8
1200.3.cy	\(\chi_{1200}(91, \cdot)\)	n/a	1920	8
1200.3.cz	\(\chi_{1200}(29, \cdot)\)	n/a	3808	8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1200))\) into lower level spaces

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