Space of modular forms of level 200 and weight 4

• Label: 200.4
• Level: 200
• Weight: 4
• Dimension: 1826
• Nonzero newspaces: 10
• Newform subspaces: 44
• Sturm bound: 9600
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 44 \)
Sturm bound:			\(9600\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(200))\).

	Total	New	Old
Modular forms	3768	1908	1860
Cusp forms	3432	1826	1606
Eisenstein series	336	82	254

Trace form

1826 * q - 14 * q^2 - 16 * q^3 - 24 * q^4 + 11 * q^5 + 8 * q^6 - 28 * q^7 + 28 * q^8 - 127 * q^9 - 16 * q^10 - 120 * q^11 - 284 * q^12 - 86 * q^13 - 260 * q^14 + 56 * q^15 + 220 * q^16 + 170 * q^17 + 942 * q^18 + 480 * q^19 + 364 * q^20 + 656 * q^21 + 424 * q^22 + 4 * q^23 - 180 * q^24 - 137 * q^25 - 496 * q^26 - 1516 * q^27 - 676 * q^28 - 1350 * q^29 + 300 * q^30 - 1220 * q^31 + 316 * q^32 - 160 * q^33 - 560 * q^34 + 452 * q^35 - 1736 * q^36 + 939 * q^37 - 2344 * q^38 + 1356 * q^39 - 1576 * q^40 + 1334 * q^41 - 3156 * q^42 + 1936 * q^43 - 1420 * q^44 + 1991 * q^45 - 1492 * q^46 - 924 * q^47 - 1316 * q^48 - 1474 * q^49 + 164 * q^50 - 3276 * q^51 + 3412 * q^52 + 307 * q^53 + 5460 * q^54 + 1592 * q^55 + 4924 * q^56 + 3360 * q^57 + 4620 * q^58 + 3232 * q^59 + 3780 * q^60 + 622 * q^61 + 5900 * q^62 + 1596 * q^63 + 8172 * q^64 - 2129 * q^65 + 8308 * q^66 + 2000 * q^67 + 1772 * q^68 - 3472 * q^69 - 1660 * q^70 - 4460 * q^71 - 10248 * q^72 - 222 * q^73 - 11492 * q^74 - 4664 * q^75 - 7344 * q^76 + 2528 * q^77 - 12820 * q^78 - 6564 * q^79 - 3676 * q^80 + 4425 * q^81 + 4288 * q^82 + 1020 * q^83 + 4492 * q^84 + 7443 * q^85 - 2720 * q^86 + 764 * q^87 + 4460 * q^88 - 3897 * q^89 - 316 * q^90 + 1636 * q^91 + 2708 * q^92 - 5720 * q^93 - 6596 * q^94 - 4608 * q^95 + 9796 * q^96 - 6850 * q^97 - 6694 * q^98 - 10128 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.4.a	\(\chi_{200}(1, \cdot)\)	200.4.a.a	1	1
		200.4.a.b	1
		200.4.a.c	1
		200.4.a.d	1
		200.4.a.e	1
		200.4.a.f	1
		200.4.a.g	1
		200.4.a.h	1
		200.4.a.i	1
		200.4.a.j	1
		200.4.a.k	2
		200.4.a.l	2
200.4.c	\(\chi_{200}(49, \cdot)\)	200.4.c.a	2	1
		200.4.c.b	2
		200.4.c.c	2
		200.4.c.d	2
		200.4.c.e	2
		200.4.c.f	2
		200.4.c.g	2
200.4.d	\(\chi_{200}(101, \cdot)\)	200.4.d.a	2	1
		200.4.d.b	12
		200.4.d.c	12
		200.4.d.d	12
		200.4.d.e	16
200.4.f	\(\chi_{200}(149, \cdot)\)	200.4.f.a	4	1
		200.4.f.b	12
		200.4.f.c	12
		200.4.f.d	24
200.4.j	\(\chi_{200}(7, \cdot)\)	None	0	2
200.4.k	\(\chi_{200}(43, \cdot)\)	200.4.k.a	2	2
		200.4.k.b	2
		200.4.k.c	2
		200.4.k.d	2
		200.4.k.e	4
		200.4.k.f	4
		200.4.k.g	8
		200.4.k.h	16
		200.4.k.i	32
		200.4.k.j	32
200.4.m	\(\chi_{200}(41, \cdot)\)	200.4.m.a	44	4
		200.4.m.b	48
200.4.o	\(\chi_{200}(29, \cdot)\)	200.4.o.a	352	4
200.4.q	\(\chi_{200}(9, \cdot)\)	200.4.q.a	88	4
200.4.t	\(\chi_{200}(21, \cdot)\)	200.4.t.a	352	4
200.4.v	\(\chi_{200}(3, \cdot)\)	200.4.v.a	704	8
200.4.w	\(\chi_{200}(23, \cdot)\)	None	0	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

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