Space of modular forms of level 200 and weight 2

• Label: 200.2
• Level: 200
• Weight: 2
• Dimension: 581
• Nonzero newspaces: 10
• Newform subspaces: 35
• Sturm bound: 4800
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 35 \)
Sturm bound:			\(4800\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(200))\).

	Total	New	Old
Modular forms	1368	663	705
Cusp forms	1033	581	452
Eisenstein series	335	82	253

Trace form

581 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 + q^5 - 20 * q^6 - 4 * q^7 - 12 * q^8 - 14 * q^9 - 16 * q^10 - 12 * q^11 - 36 * q^12 + 4 * q^13 - 36 * q^14 - 24 * q^15 - 52 * q^16 - 28 * q^17 - 68 * q^18 - 44 * q^19 - 36 * q^20 - 16 * q^21 - 52 * q^22 - 20 * q^23 - 68 * q^24 - 27 * q^25 - 72 * q^26 - 36 * q^27 - 4 * q^28 + 12 * q^29 - 20 * q^30 - 36 * q^31 + 28 * q^32 - 24 * q^33 + 52 * q^34 - 28 * q^35 + 44 * q^36 - 17 * q^37 + 28 * q^38 - 76 * q^39 + 24 * q^40 - 56 * q^41 + 28 * q^42 - 100 * q^43 + 12 * q^44 - 79 * q^45 + 28 * q^46 - 108 * q^47 - 4 * q^48 - 99 * q^49 - 36 * q^50 - 132 * q^51 - 60 * q^52 - 57 * q^53 - 68 * q^54 - 88 * q^55 - 132 * q^56 - 152 * q^57 - 108 * q^58 - 100 * q^59 - 60 * q^60 + 24 * q^61 - 132 * q^62 - 44 * q^63 - 84 * q^64 - 59 * q^65 - 68 * q^66 + 20 * q^67 - 60 * q^68 - 16 * q^69 - 20 * q^70 + 12 * q^71 + 64 * q^72 - 92 * q^73 + 20 * q^74 + 56 * q^75 + 8 * q^76 + 32 * q^77 + 108 * q^78 + 140 * q^79 + 4 * q^80 - 78 * q^81 + 132 * q^82 + 160 * q^83 + 204 * q^84 + 73 * q^85 + 68 * q^86 + 196 * q^87 + 220 * q^88 - 53 * q^89 + 284 * q^90 + 116 * q^91 + 212 * q^92 + 120 * q^93 + 236 * q^94 + 112 * q^95 + 68 * q^96 + 48 * q^97 + 236 * q^98 + 188 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.2.a	\(\chi_{200}(1, \cdot)\)	200.2.a.a	1	1
		200.2.a.b	1
		200.2.a.c	1
		200.2.a.d	1
		200.2.a.e	1
200.2.c	\(\chi_{200}(49, \cdot)\)	200.2.c.a	2	1
		200.2.c.b	2
200.2.d	\(\chi_{200}(101, \cdot)\)	200.2.d.a	2	1
		200.2.d.b	2
		200.2.d.c	2
		200.2.d.d	2
		200.2.d.e	4
		200.2.d.f	4
200.2.f	\(\chi_{200}(149, \cdot)\)	200.2.f.a	2	1
		200.2.f.b	2
		200.2.f.c	4
		200.2.f.d	4
		200.2.f.e	4
200.2.j	\(\chi_{200}(7, \cdot)\)	None	0	2
200.2.k	\(\chi_{200}(43, \cdot)\)	200.2.k.a	2	2
		200.2.k.b	2
		200.2.k.c	2
		200.2.k.d	2
		200.2.k.e	4
		200.2.k.f	4
		200.2.k.g	8
		200.2.k.h	8
200.2.m	\(\chi_{200}(41, \cdot)\)	200.2.m.a	4	4
		200.2.m.b	8
		200.2.m.c	16
200.2.o	\(\chi_{200}(29, \cdot)\)	200.2.o.a	112	4
200.2.q	\(\chi_{200}(9, \cdot)\)	200.2.q.a	32	4
200.2.t	\(\chi_{200}(21, \cdot)\)	200.2.t.a	112	4
200.2.v	\(\chi_{200}(3, \cdot)\)	200.2.v.a	8	8
		200.2.v.b	8
		200.2.v.c	208
200.2.w	\(\chi_{200}(23, \cdot)\)	None	0	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

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