Space of modular forms of level 200 and weight 6

• Label: 200.6
• Level: 200
• Weight: 6
• Dimension: 3070
• Nonzero newspaces: 10
• Sturm bound: 14400
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(14400\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(200))\).

	Total	New	Old
Modular forms	6168	3152	3016
Cusp forms	5832	3070	2762
Eisenstein series	336	82	254

Trace form

3070 * q - 14 * q^2 + 8 * q^3 + 8 * q^4 + 41 * q^5 - 136 * q^6 - 92 * q^7 - 260 * q^8 + 779 * q^9 - 16 * q^10 + 144 * q^11 - 380 * q^12 - 1878 * q^13 + 3100 * q^14 + 2456 * q^15 - 292 * q^16 + 614 * q^17 - 10434 * q^18 - 5640 * q^19 - 6836 * q^20 - 1360 * q^21 - 4488 * q^22 - 380 * q^23 + 25740 * q^24 - 247 * q^25 + 29408 * q^26 + 15044 * q^27 + 348 * q^28 - 8790 * q^29 - 9780 * q^30 + 19644 * q^31 - 45764 * q^32 + 22664 * q^33 - 54000 * q^34 - 10348 * q^35 + 15736 * q^36 - 62491 * q^37 + 90248 * q^38 - 51252 * q^39 + 59224 * q^40 - 4774 * q^41 + 28524 * q^42 + 24152 * q^43 - 78700 * q^44 + 15341 * q^45 - 232180 * q^46 - 3804 * q^47 - 116708 * q^48 + 39098 * q^49 + 103364 * q^50 + 58740 * q^51 + 323380 * q^52 - 23891 * q^53 + 138420 * q^54 + 60312 * q^55 - 150212 * q^56 + 93576 * q^57 - 302564 * q^58 - 200024 * q^59 - 201180 * q^60 - 111962 * q^61 - 235636 * q^62 - 288612 * q^63 + 242156 * q^64 - 75719 * q^65 + 338164 * q^66 + 129768 * q^67 + 262124 * q^68 + 441104 * q^69 + 34980 * q^70 + 189268 * q^71 - 219528 * q^72 + 338238 * q^73 - 278516 * q^74 - 54584 * q^75 - 31056 * q^76 - 448864 * q^77 + 653324 * q^78 - 181412 * q^79 + 233924 * q^80 - 1074297 * q^81 + 1447904 * q^82 + 545604 * q^83 + 492556 * q^84 - 134767 * q^85 - 384080 * q^86 - 506692 * q^87 - 2166676 * q^88 + 1043529 * q^89 - 2325916 * q^90 - 306012 * q^91 - 1052524 * q^92 + 340600 * q^93 + 140732 * q^94 + 412992 * q^95 + 653572 * q^96 - 651822 * q^97 + 2392634 * q^98 + 286056 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.6.a	\(\chi_{200}(1, \cdot)\)	200.6.a.a	1	1
		200.6.a.b	1
		200.6.a.c	1
		200.6.a.d	1
		200.6.a.e	2
		200.6.a.f	2
		200.6.a.g	2
		200.6.a.h	3
		200.6.a.i	3
		200.6.a.j	4
		200.6.a.k	4
200.6.c	\(\chi_{200}(49, \cdot)\)	200.6.c.a	2	1
		200.6.c.b	2
		200.6.c.c	2
		200.6.c.d	2
		200.6.c.e	4
		200.6.c.f	4
		200.6.c.g	6
200.6.d	\(\chi_{200}(101, \cdot)\)	200.6.d.a	4	1
		200.6.d.b	20
		200.6.d.c	20
		200.6.d.d	20
		200.6.d.e	28
200.6.f	\(\chi_{200}(149, \cdot)\)	200.6.f.a	8	1
		200.6.f.b	20
		200.6.f.c	20
		200.6.f.d	40
200.6.j	\(\chi_{200}(7, \cdot)\)	None	0	2
200.6.k	\(\chi_{200}(43, \cdot)\)	n/a	176	2
200.6.m	\(\chi_{200}(41, \cdot)\)	n/a	148	4
200.6.o	\(\chi_{200}(29, \cdot)\)	n/a	592	4
200.6.q	\(\chi_{200}(9, \cdot)\)	n/a	152	4
200.6.t	\(\chi_{200}(21, \cdot)\)	n/a	592	4
200.6.v	\(\chi_{200}(3, \cdot)\)	n/a	1184	8
200.6.w	\(\chi_{200}(23, \cdot)\)	None	0	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

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