Space of modular forms of level 200 and weight 9

• Label: 200.9
• Level: 200
• Weight: 9
• Dimension: 4935
• Nonzero newspaces: 8
• Sturm bound: 21600
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(21600\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(200))\).

	Total	New	Old
Modular forms	9768	5017	4751
Cusp forms	9432	4935	4497
Eisenstein series	336	82	254

Trace form

4935 * q - 10 * q^2 - 14 * q^3 - 344 * q^4 + 336 * q^5 - 760 * q^6 + 308 * q^7 - 2740 * q^8 + 10909 * q^9 - 16 * q^10 - 3862 * q^11 + 33844 * q^12 + 9520 * q^13 + 86124 * q^14 + 111056 * q^15 + 48476 * q^16 - 26 * q^17 - 949422 * q^18 - 167558 * q^19 + 562364 * q^20 + 1585472 * q^21 + 694136 * q^22 - 1374732 * q^23 - 2863572 * q^24 - 367912 * q^25 + 862568 * q^26 + 5173048 * q^27 + 1967260 * q^28 + 2547100 * q^30 - 3658388 * q^31 - 3375940 * q^32 + 4788548 * q^33 - 1393032 * q^34 + 751952 * q^35 + 7880264 * q^36 - 255520 * q^37 + 2252664 * q^38 - 22510420 * q^39 - 9609576 * q^40 + 12778086 * q^41 - 18630932 * q^42 + 25710322 * q^43 - 17620668 * q^44 - 32525384 * q^45 + 53858268 * q^46 - 84052812 * q^47 - 649924 * q^48 - 6890705 * q^49 + 10668164 * q^50 + 121857844 * q^51 + 24137188 * q^52 + 12598560 * q^53 - 46059244 * q^54 - 41341108 * q^55 - 139549892 * q^56 - 98503276 * q^57 - 64372092 * q^58 - 46728198 * q^59 + 49439380 * q^60 - 45412608 * q^61 + 223926828 * q^62 + 159934372 * q^63 + 58411756 * q^64 - 71394104 * q^65 + 79959076 * q^66 + 41337586 * q^67 - 371309684 * q^68 - 199704060 * q^70 - 187630484 * q^71 + 66426776 * q^72 - 95956986 * q^73 + 436690884 * q^74 + 253051536 * q^75 + 108809408 * q^76 - 56834880 * q^77 + 441309212 * q^78 - 20 * q^79 - 80941676 * q^80 + 479454123 * q^81 - 729298376 * q^82 + 61414066 * q^83 + 418937420 * q^84 + 354033168 * q^85 + 96241904 * q^86 + 276611196 * q^87 - 758150164 * q^88 - 676414178 * q^89 - 873084316 * q^90 - 181525524 * q^91 + 478702420 * q^92 + 349443840 * q^93 + 1105514844 * q^94 + 378791892 * q^95 - 968898716 * q^96 + 215773030 * q^97 + 1008668622 * q^98 + 1133900018 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.9.b	\(\chi_{200}(151, \cdot)\)	None	0	1
200.9.e	\(\chi_{200}(99, \cdot)\)	n/a	142	1
200.9.g	\(\chi_{200}(51, \cdot)\)	n/a	149	1
200.9.h	\(\chi_{200}(199, \cdot)\)	None	0	1
200.9.i	\(\chi_{200}(93, \cdot)\)	n/a	284	2
200.9.l	\(\chi_{200}(57, \cdot)\)	200.9.l.a	8	2
		200.9.l.b	8
		200.9.l.c	12
		200.9.l.d	12
		200.9.l.e	16
		200.9.l.f	16
200.9.n	\(\chi_{200}(11, \cdot)\)	n/a	952	4
200.9.p	\(\chi_{200}(39, \cdot)\)	None	0	4
200.9.r	\(\chi_{200}(31, \cdot)\)	None	0	4
200.9.s	\(\chi_{200}(19, \cdot)\)	n/a	952	4
200.9.u	\(\chi_{200}(17, \cdot)\)	n/a	480	8
200.9.x	\(\chi_{200}(13, \cdot)\)	n/a	1904	8

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

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