Space of modular forms of level 800 and weight 4

• Label: 800.4
• Level: 800
• Weight: 4
• Dimension: 29657
• Nonzero newspaces: 20
• Sturm bound: 153600
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(153600\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(800))\).

	Total	New	Old
Modular forms	58496	30067	28429
Cusp forms	56704	29657	27047
Eisenstein series	1792	410	1382

Trace form

29657 * q - 52 * q^2 - 40 * q^3 - 52 * q^4 - 64 * q^5 - 84 * q^6 - 24 * q^7 - 52 * q^8 - 31 * q^9 - 64 * q^10 - 64 * q^11 - 100 * q^12 - 170 * q^13 - 260 * q^14 - 48 * q^15 - 384 * q^16 - 206 * q^17 - 232 * q^18 - 32 * q^19 - 64 * q^20 + 172 * q^21 + 144 * q^22 + 592 * q^23 - 96 * q^24 - 96 * q^25 - 144 * q^26 - 88 * q^27 + 328 * q^28 + 886 * q^29 - 64 * q^30 - 204 * q^31 + 568 * q^32 - 408 * q^33 + 480 * q^34 - 504 * q^35 + 1376 * q^36 - 1858 * q^37 + 932 * q^38 - 1384 * q^39 - 64 * q^40 - 2042 * q^41 - 2312 * q^42 - 960 * q^43 - 2092 * q^44 - 424 * q^45 - 1524 * q^46 + 108 * q^47 - 2496 * q^48 + 2165 * q^49 - 64 * q^50 + 1472 * q^51 - 2572 * q^52 + 2686 * q^53 - 1136 * q^54 + 452 * q^55 + 1112 * q^56 + 524 * q^57 + 3152 * q^58 + 1344 * q^59 - 1088 * q^60 - 1018 * q^61 + 3336 * q^62 - 68 * q^63 - 10552 * q^64 - 4352 * q^65 - 20452 * q^66 - 1696 * q^67 - 9152 * q^68 - 6292 * q^69 - 1648 * q^70 + 752 * q^71 + 9284 * q^72 + 3910 * q^73 + 13724 * q^74 + 3256 * q^75 + 11868 * q^76 + 14588 * q^77 + 34852 * q^78 + 7172 * q^79 + 12576 * q^80 + 18173 * q^81 + 16908 * q^82 + 7760 * q^83 + 29264 * q^84 + 4640 * q^85 + 8464 * q^86 - 216 * q^87 + 3664 * q^88 - 3274 * q^89 - 7504 * q^90 - 7056 * q^91 - 12072 * q^92 - 14816 * q^93 - 16552 * q^94 - 3412 * q^95 - 31696 * q^96 - 12294 * q^97 - 14072 * q^98 - 5472 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(800))\)

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
800.4.a	\(\chi_{800}(1, \cdot)\)	800.4.a.a	1	1
		800.4.a.b	1
		800.4.a.c	1
		800.4.a.d	1
		800.4.a.e	1
		800.4.a.f	1
		800.4.a.g	1
		800.4.a.h	1
		800.4.a.i	1
		800.4.a.j	1
		800.4.a.k	1
		800.4.a.l	2
		800.4.a.m	2
		800.4.a.n	2
		800.4.a.o	2
		800.4.a.p	2
		800.4.a.q	2
		800.4.a.r	2
		800.4.a.s	2
		800.4.a.t	2
		800.4.a.u	3
		800.4.a.v	3
		800.4.a.w	3
		800.4.a.x	3
		800.4.a.y	4
		800.4.a.z	4
		800.4.a.ba	4
		800.4.a.bb	4
800.4.c	\(\chi_{800}(449, \cdot)\)	800.4.c.a	2	1
		800.4.c.b	2
		800.4.c.c	2
		800.4.c.d	2
		800.4.c.e	2
		800.4.c.f	2
		800.4.c.g	2
		800.4.c.h	4
		800.4.c.i	4
		800.4.c.j	4
		800.4.c.k	4
		800.4.c.l	4
		800.4.c.m	6
		800.4.c.n	6
		800.4.c.o	8
800.4.d	\(\chi_{800}(401, \cdot)\)	800.4.d.a	2	1
		800.4.d.b	12
		800.4.d.c	12
		800.4.d.d	12
		800.4.d.e	16
800.4.f	\(\chi_{800}(49, \cdot)\)	800.4.f.a	4	1
		800.4.f.b	12
		800.4.f.c	12
		800.4.f.d	24
800.4.j	\(\chi_{800}(407, \cdot)\)	None	0	2
800.4.l	\(\chi_{800}(201, \cdot)\)	None	0	2
800.4.n	\(\chi_{800}(543, \cdot)\)	n/a	108	2
800.4.o	\(\chi_{800}(143, \cdot)\)	n/a	104	2
800.4.q	\(\chi_{800}(249, \cdot)\)	None	0	2
800.4.s	\(\chi_{800}(7, \cdot)\)	None	0	2
800.4.u	\(\chi_{800}(161, \cdot)\)	n/a	360	4
800.4.v	\(\chi_{800}(43, \cdot)\)	n/a	856	4
800.4.y	\(\chi_{800}(101, \cdot)\)	n/a	900	4
800.4.ba	\(\chi_{800}(149, \cdot)\)	n/a	856	4
800.4.bb	\(\chi_{800}(107, \cdot)\)	n/a	856	4
800.4.be	\(\chi_{800}(209, \cdot)\)	n/a	352	4
800.4.bg	\(\chi_{800}(129, \cdot)\)	n/a	360	4
800.4.bj	\(\chi_{800}(81, \cdot)\)	n/a	352	4
800.4.bl	\(\chi_{800}(23, \cdot)\)	None	0	8
800.4.bm	\(\chi_{800}(41, \cdot)\)	None	0	8
800.4.bp	\(\chi_{800}(47, \cdot)\)	n/a	704	8
800.4.bq	\(\chi_{800}(63, \cdot)\)	n/a	720	8
800.4.bt	\(\chi_{800}(9, \cdot)\)	None	0	8
800.4.bu	\(\chi_{800}(87, \cdot)\)	None	0	8
800.4.bx	\(\chi_{800}(67, \cdot)\)	n/a	5728	16
800.4.by	\(\chi_{800}(29, \cdot)\)	n/a	5728	16
800.4.ca	\(\chi_{800}(21, \cdot)\)	n/a	5728	16
800.4.cd	\(\chi_{800}(3, \cdot)\)	n/a	5728	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(800))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(800)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)