Space of modular forms of level 200 and weight 5

• Label: 200.5
• Level: 200
• Weight: 5
• Dimension: 2447
• Nonzero newspaces: 8
• Sturm bound: 12000
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(12000\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(200))\).

	Total	New	Old
Modular forms	4968	2529	2439
Cusp forms	4632	2447	2185
Eisenstein series	336	82	254

Trace form

2447 * q - 10 * q^2 - 14 * q^3 - 24 * q^4 - 24 * q^5 - 88 * q^6 + 148 * q^7 + 140 * q^8 + q^9 - 16 * q^10 - 406 * q^11 + 244 * q^12 - 40 * q^13 - 852 * q^14 - 544 * q^15 - 1700 * q^16 - 26 * q^17 - 1422 * q^18 + 698 * q^19 + 764 * q^20 + 416 * q^21 + 4056 * q^22 + 3828 * q^23 + 6060 * q^24 + 1308 * q^25 + 392 * q^26 - 872 * q^27 - 6500 * q^28 - 5540 * q^30 - 1364 * q^31 + 3260 * q^32 - 8812 * q^33 + 11000 * q^34 - 7648 * q^35 + 15176 * q^36 - 2960 * q^37 + 5784 * q^38 + 8780 * q^39 - 3176 * q^40 + 10398 * q^41 - 20372 * q^42 + 3442 * q^43 - 15612 * q^44 - 14084 * q^45 - 868 * q^46 + 21588 * q^47 + 4796 * q^48 - 501 * q^49 - 2236 * q^50 - 17660 * q^51 - 3292 * q^52 - 7920 * q^53 - 33196 * q^54 - 2148 * q^55 - 28868 * q^56 - 316 * q^57 - 8412 * q^58 - 3078 * q^59 + 6100 * q^60 + 11136 * q^61 + 31788 * q^62 + 5572 * q^63 + 18156 * q^64 + 21076 * q^65 + 37156 * q^66 + 40306 * q^67 + 45196 * q^68 + 27460 * q^70 + 34348 * q^71 + 56216 * q^72 - 97546 * q^73 + 3108 * q^74 - 9024 * q^75 - 6656 * q^76 - 20640 * q^77 + 11612 * q^78 - 20 * q^79 - 8876 * q^80 + 60735 * q^81 - 146056 * q^82 - 55214 * q^83 - 187060 * q^84 + 9288 * q^85 - 64432 * q^86 - 36804 * q^87 + 6636 * q^88 + 59458 * q^89 + 174884 * q^90 - 45076 * q^91 + 92500 * q^92 + 1920 * q^93 + 203868 * q^94 + 75492 * q^95 + 92644 * q^96 - 51290 * q^97 + 101262 * q^98 + 102002 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.5.b	\(\chi_{200}(151, \cdot)\)	None	0	1
200.5.e	\(\chi_{200}(99, \cdot)\)	200.5.e.a	2	1
		200.5.e.b	4
		200.5.e.c	4
		200.5.e.d	28
		200.5.e.e	32
200.5.g	\(\chi_{200}(51, \cdot)\)	200.5.g.a	1	1
		200.5.g.b	2
		200.5.g.c	2
		200.5.g.d	2
		200.5.g.e	2
		200.5.g.f	14
		200.5.g.g	14
		200.5.g.h	16
		200.5.g.i	20
200.5.h	\(\chi_{200}(199, \cdot)\)	None	0	1
200.5.i	\(\chi_{200}(93, \cdot)\)	n/a	140	2
200.5.l	\(\chi_{200}(57, \cdot)\)	200.5.l.a	2	2
		200.5.l.b	4
		200.5.l.c	4
		200.5.l.d	4
		200.5.l.e	6
		200.5.l.f	8
		200.5.l.g	8
200.5.n	\(\chi_{200}(11, \cdot)\)	n/a	472	4
200.5.p	\(\chi_{200}(39, \cdot)\)	None	0	4
200.5.r	\(\chi_{200}(31, \cdot)\)	None	0	4
200.5.s	\(\chi_{200}(19, \cdot)\)	n/a	472	4
200.5.u	\(\chi_{200}(17, \cdot)\)	n/a	240	8
200.5.x	\(\chi_{200}(13, \cdot)\)	n/a	944	8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

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