Space of modular forms of level 1200 and weight 2

• Label: 1200.2
• Level: 1200
• Weight: 2
• Dimension: 14747
• Nonzero newspaces: 28
• Sturm bound: 153600
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(153600\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1200))\).

	Total	New	Old
Modular forms	39968	15115	24853
Cusp forms	36833	14747	22086
Eisenstein series	3135	368	2767

Trace form

14747 * q - 19 * q^3 - 56 * q^4 - 48 * q^6 - 44 * q^7 - 12 * q^8 - 15 * q^9 - 64 * q^10 - 12 * q^11 - 24 * q^12 - 86 * q^13 + 12 * q^14 - 36 * q^15 - 64 * q^16 - 30 * q^17 - 16 * q^18 - 92 * q^19 - 78 * q^21 - 32 * q^22 - 40 * q^23 + 4 * q^24 - 32 * q^25 + 20 * q^26 - 31 * q^27 + 80 * q^28 + 6 * q^29 - 12 * q^31 + 160 * q^32 - 10 * q^33 + 200 * q^34 + 24 * q^35 + 8 * q^36 + 66 * q^37 + 216 * q^38 + 52 * q^39 + 96 * q^40 + 122 * q^41 + 92 * q^42 + 28 * q^43 + 184 * q^44 - 14 * q^45 + 128 * q^46 + 48 * q^47 + 40 * q^48 - 13 * q^49 + 80 * q^50 + 38 * q^51 + 48 * q^52 + 46 * q^53 - 72 * q^54 - 28 * q^55 + 38 * q^57 - 32 * q^58 + 28 * q^59 - 64 * q^60 - 46 * q^61 - 12 * q^62 + 202 * q^63 - 80 * q^64 + 8 * q^65 - 116 * q^66 + 220 * q^67 - 192 * q^68 + 90 * q^69 - 208 * q^70 + 312 * q^71 - 228 * q^72 + 2 * q^73 - 300 * q^74 + 128 * q^75 - 352 * q^76 + 112 * q^77 - 312 * q^78 + 324 * q^79 - 160 * q^80 - 51 * q^81 - 280 * q^82 + 436 * q^83 - 336 * q^84 + 128 * q^85 - 272 * q^86 + 268 * q^87 - 432 * q^88 + 74 * q^89 - 152 * q^90 + 244 * q^91 - 304 * q^92 + 110 * q^93 - 312 * q^94 + 312 * q^95 - 224 * q^96 + 66 * q^97 - 136 * q^98 + 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)

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
1200.2.a	\(\chi_{1200}(1, \cdot)\)	1200.2.a.a	1	1
		1200.2.a.b	1
		1200.2.a.c	1
		1200.2.a.d	1
		1200.2.a.e	1
		1200.2.a.f	1
		1200.2.a.g	1
		1200.2.a.h	1
		1200.2.a.i	1
		1200.2.a.j	1
		1200.2.a.k	1
		1200.2.a.l	1
		1200.2.a.m	1
		1200.2.a.n	1
		1200.2.a.o	1
		1200.2.a.p	1
		1200.2.a.q	1
		1200.2.a.r	1
		1200.2.a.s	1
1200.2.b	\(\chi_{1200}(551, \cdot)\)	None	0	1
1200.2.d	\(\chi_{1200}(649, \cdot)\)	None	0	1
1200.2.f	\(\chi_{1200}(49, \cdot)\)	1200.2.f.a	2	1
		1200.2.f.b	2
		1200.2.f.c	2
		1200.2.f.d	2
		1200.2.f.e	2
		1200.2.f.f	2
		1200.2.f.g	2
		1200.2.f.h	2
		1200.2.f.i	2
1200.2.h	\(\chi_{1200}(1151, \cdot)\)	1200.2.h.a	2	1
		1200.2.h.b	2
		1200.2.h.c	2
		1200.2.h.d	2
		1200.2.h.e	2
		1200.2.h.f	2
		1200.2.h.g	2
		1200.2.h.h	2
		1200.2.h.i	2
		1200.2.h.j	4
		1200.2.h.k	4
		1200.2.h.l	4
		1200.2.h.m	4
		1200.2.h.n	4
1200.2.k	\(\chi_{1200}(601, \cdot)\)	None	0	1
1200.2.m	\(\chi_{1200}(599, \cdot)\)	None	0	1
1200.2.o	\(\chi_{1200}(1199, \cdot)\)	1200.2.o.a	4	1
		1200.2.o.b	4
		1200.2.o.c	4
		1200.2.o.d	4
		1200.2.o.e	4
		1200.2.o.f	4
		1200.2.o.g	4
		1200.2.o.h	4
		1200.2.o.i	4
1200.2.s	\(\chi_{1200}(301, \cdot)\)	n/a	152	2
1200.2.t	\(\chi_{1200}(299, \cdot)\)	n/a	280	2
1200.2.v	\(\chi_{1200}(257, \cdot)\)	1200.2.v.a	4	2
		1200.2.v.b	4
		1200.2.v.c	4
		1200.2.v.d	4
		1200.2.v.e	4
		1200.2.v.f	4
		1200.2.v.g	4
		1200.2.v.h	4
		1200.2.v.i	4
		1200.2.v.j	4
		1200.2.v.k	4
		1200.2.v.l	8
		1200.2.v.m	16
1200.2.w	\(\chi_{1200}(607, \cdot)\)	1200.2.w.a	4	2
		1200.2.w.b	8
		1200.2.w.c	8
		1200.2.w.d	8
		1200.2.w.e	8
1200.2.y	\(\chi_{1200}(643, \cdot)\)	n/a	144	2
1200.2.bb	\(\chi_{1200}(893, \cdot)\)	n/a	280	2
1200.2.bc	\(\chi_{1200}(43, \cdot)\)	n/a	144	2
1200.2.bf	\(\chi_{1200}(293, \cdot)\)	n/a	280	2
1200.2.bh	\(\chi_{1200}(7, \cdot)\)	None	0	2
1200.2.bi	\(\chi_{1200}(857, \cdot)\)	None	0	2
1200.2.bk	\(\chi_{1200}(251, \cdot)\)	n/a	292	2
1200.2.bl	\(\chi_{1200}(349, \cdot)\)	n/a	144	2
1200.2.bo	\(\chi_{1200}(241, \cdot)\)	n/a	120	4
1200.2.bq	\(\chi_{1200}(191, \cdot)\)	n/a	240	4
1200.2.bs	\(\chi_{1200}(289, \cdot)\)	n/a	120	4
1200.2.bu	\(\chi_{1200}(169, \cdot)\)	None	0	4
1200.2.bw	\(\chi_{1200}(71, \cdot)\)	None	0	4
1200.2.by	\(\chi_{1200}(239, \cdot)\)	n/a	240	4
1200.2.ca	\(\chi_{1200}(119, \cdot)\)	None	0	4
1200.2.cc	\(\chi_{1200}(121, \cdot)\)	None	0	4
1200.2.ce	\(\chi_{1200}(59, \cdot)\)	n/a	1888	8
1200.2.cf	\(\chi_{1200}(61, \cdot)\)	n/a	960	8
1200.2.cj	\(\chi_{1200}(137, \cdot)\)	None	0	8
1200.2.ck	\(\chi_{1200}(103, \cdot)\)	None	0	8
1200.2.cm	\(\chi_{1200}(53, \cdot)\)	n/a	1888	8
1200.2.cp	\(\chi_{1200}(67, \cdot)\)	n/a	960	8
1200.2.cq	\(\chi_{1200}(173, \cdot)\)	n/a	1888	8
1200.2.ct	\(\chi_{1200}(163, \cdot)\)	n/a	960	8
1200.2.cv	\(\chi_{1200}(127, \cdot)\)	n/a	240	8
1200.2.cw	\(\chi_{1200}(17, \cdot)\)	n/a	464	8
1200.2.da	\(\chi_{1200}(109, \cdot)\)	n/a	960	8
1200.2.db	\(\chi_{1200}(11, \cdot)\)	n/a	1888	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1200))\) into lower level spaces

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