Space of modular forms of level 200 and weight 3

• Label: 200.3
• Level: 200
• Weight: 3
• Dimension: 1203
• Nonzero newspaces: 8
• Newform subspaces: 26
• Sturm bound: 7200
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(7200\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(200))\).

	Total	New	Old
Modular forms	2568	1285	1283
Cusp forms	2232	1203	1029
Eisenstein series	336	82	254

Trace form

1203 * q - 14 * q^2 - 14 * q^3 - 8 * q^4 - 4 * q^5 - 16 * q^6 - 28 * q^7 - 20 * q^8 - 29 * q^9 - 16 * q^10 + 10 * q^11 + 52 * q^12 + 76 * q^13 + 108 * q^14 + 56 * q^15 + 92 * q^16 + 6 * q^17 + 54 * q^18 - 38 * q^19 - 36 * q^20 - 112 * q^21 - 160 * q^22 - 204 * q^23 - 276 * q^24 - 82 * q^25 - 264 * q^26 - 152 * q^27 - 356 * q^28 - 260 * q^30 + 268 * q^31 - 324 * q^32 + 188 * q^33 - 336 * q^34 + 152 * q^35 - 232 * q^36 + 224 * q^37 + 32 * q^38 + 380 * q^39 + 24 * q^40 - 38 * q^41 + 268 * q^42 - 110 * q^43 + 452 * q^44 + 166 * q^45 + 636 * q^46 - 60 * q^47 + 1148 * q^48 + 25 * q^49 + 564 * q^50 - 68 * q^51 + 964 * q^52 - 48 * q^53 + 740 * q^54 - 268 * q^55 + 316 * q^56 - 292 * q^57 + 84 * q^58 - 486 * q^59 - 140 * q^60 - 192 * q^61 - 372 * q^62 - 1292 * q^63 - 788 * q^64 - 134 * q^65 - 1580 * q^66 - 974 * q^67 - 1556 * q^68 - 780 * q^70 - 1076 * q^71 - 1960 * q^72 - 18 * q^73 - 1292 * q^74 - 504 * q^75 - 640 * q^76 - 144 * q^77 - 484 * q^78 - 20 * q^79 - 76 * q^80 - 87 * q^81 - 464 * q^82 - 126 * q^83 - 820 * q^84 - 852 * q^85 + 88 * q^86 + 156 * q^87 - 916 * q^88 - 828 * q^89 - 1516 * q^90 + 492 * q^91 - 44 * q^92 - 960 * q^93 - 132 * q^94 + 92 * q^95 + 1060 * q^96 - 602 * q^97 - 214 * q^98 + 1202 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.3.b	\(\chi_{200}(151, \cdot)\)	None	0	1
200.3.e	\(\chi_{200}(99, \cdot)\)	200.3.e.a	2	1
		200.3.e.b	4
		200.3.e.c	12
		200.3.e.d	16
200.3.g	\(\chi_{200}(51, \cdot)\)	200.3.g.a	1	1
		200.3.g.b	2
		200.3.g.c	2
		200.3.g.d	2
		200.3.g.e	6
		200.3.g.f	6
		200.3.g.g	8
		200.3.g.h	8
200.3.h	\(\chi_{200}(199, \cdot)\)	None	0	1
200.3.i	\(\chi_{200}(93, \cdot)\)	200.3.i.a	16	2
		200.3.i.b	20
		200.3.i.c	32
200.3.l	\(\chi_{200}(57, \cdot)\)	200.3.l.a	2	2
		200.3.l.b	2
		200.3.l.c	2
		200.3.l.d	4
		200.3.l.e	4
		200.3.l.f	4
200.3.n	\(\chi_{200}(11, \cdot)\)	200.3.n.a	232	4
200.3.p	\(\chi_{200}(39, \cdot)\)	None	0	4
200.3.r	\(\chi_{200}(31, \cdot)\)	None	0	4
200.3.s	\(\chi_{200}(19, \cdot)\)	200.3.s.a	232	4
200.3.u	\(\chi_{200}(17, \cdot)\)	200.3.u.a	56	8
		200.3.u.b	64
200.3.x	\(\chi_{200}(13, \cdot)\)	200.3.x.a	464	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(200)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)