Space of modular forms of level 800 and weight 6

• Label: 800.6
• Level: 800
• Weight: 6
• Dimension: 49565
• Nonzero newspaces: 20
• Sturm bound: 230400
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(230400\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(800))\).

	Total	New	Old
Modular forms	96896	49975	46921
Cusp forms	95104	49565	45539
Eisenstein series	1792	410	1382

Trace form

49565 * q - 52 * q^2 - 40 * q^3 - 52 * q^4 - 64 * q^5 - 84 * q^6 - 136 * q^7 - 52 * q^8 + 209 * q^9 - 64 * q^10 - 64 * q^11 - 1636 * q^12 + 58 * q^13 + 2428 * q^14 - 48 * q^15 + 4096 * q^16 + 1786 * q^17 - 1672 * q^18 - 32 * q^19 - 64 * q^20 - 5972 * q^21 - 12432 * q^22 - 704 * q^23 + 21408 * q^24 - 96 * q^25 + 12816 * q^26 - 5560 * q^27 - 2232 * q^28 + 37882 * q^29 - 64 * q^30 + 7284 * q^31 - 18632 * q^32 - 64752 * q^33 - 6304 * q^34 - 4824 * q^35 + 65504 * q^36 + 67970 * q^37 + 356 * q^38 + 17288 * q^39 - 64 * q^40 + 41662 * q^41 - 53672 * q^42 + 34656 * q^43 + 3668 * q^44 - 61624 * q^45 + 63244 * q^46 - 75828 * q^47 + 112320 * q^48 - 79543 * q^49 - 64 * q^50 + 21728 * q^51 + 18420 * q^52 + 34978 * q^53 + 1264 * q^54 + 12452 * q^55 - 81064 * q^56 - 138988 * q^57 - 84624 * q^58 - 28992 * q^59 - 16448 * q^60 + 204586 * q^61 + 63432 * q^62 - 137876 * q^63 - 1155256 * q^64 - 141632 * q^65 - 5572 * q^66 + 117312 * q^67 + 1062592 * q^68 + 869036 * q^69 + 798992 * q^70 + 224768 * q^71 + 1466564 * q^72 + 80734 * q^73 + 19100 * q^74 - 127784 * q^75 - 718244 * q^76 - 783652 * q^77 - 3473948 * q^78 - 251484 * q^79 - 985824 * q^80 - 1135207 * q^81 - 1033972 * q^82 - 582160 * q^83 - 242224 * q^84 + 63200 * q^85 + 998128 * q^86 - 23784 * q^87 + 2291920 * q^88 + 864302 * q^89 + 2382896 * q^90 + 858928 * q^91 + 2119896 * q^92 + 1614400 * q^93 + 631896 * q^94 - 25972 * q^95 - 2934736 * q^96 - 1026526 * q^97 - 3639608 * q^98 + 338496 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(800))\)

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
800.6.a	\(\chi_{800}(1, \cdot)\)	800.6.a.a	1	1
		800.6.a.b	1
		800.6.a.c	1
		800.6.a.d	1
		800.6.a.e	1
		800.6.a.f	2
		800.6.a.g	2
		800.6.a.h	2
		800.6.a.i	2
		800.6.a.j	2
		800.6.a.k	2
		800.6.a.l	2
		800.6.a.m	2
		800.6.a.n	3
		800.6.a.o	3
		800.6.a.p	4
		800.6.a.q	4
		800.6.a.r	4
		800.6.a.s	5
		800.6.a.t	5
		800.6.a.u	5
		800.6.a.v	5
		800.6.a.w	6
		800.6.a.x	6
		800.6.a.y	6
		800.6.a.z	6
		800.6.a.ba	6
		800.6.a.bb	6
800.6.c	\(\chi_{800}(449, \cdot)\)	800.6.c.a	2	1
		800.6.c.b	2
		800.6.c.c	2
		800.6.c.d	4
		800.6.c.e	4
		800.6.c.f	4
		800.6.c.g	4
		800.6.c.h	4
		800.6.c.i	4
		800.6.c.j	6
		800.6.c.k	6
		800.6.c.l	8
		800.6.c.m	8
		800.6.c.n	10
		800.6.c.o	10
		800.6.c.p	12
800.6.d	\(\chi_{800}(401, \cdot)\)	800.6.d.a	4	1
		800.6.d.b	20
		800.6.d.c	20
		800.6.d.d	20
		800.6.d.e	28
800.6.f	\(\chi_{800}(49, \cdot)\)	800.6.f.a	8	1
		800.6.f.b	20
		800.6.f.c	20
		800.6.f.d	40
800.6.j	\(\chi_{800}(407, \cdot)\)	None	0	2
800.6.l	\(\chi_{800}(201, \cdot)\)	None	0	2
800.6.n	\(\chi_{800}(543, \cdot)\)	n/a	180	2
800.6.o	\(\chi_{800}(143, \cdot)\)	n/a	176	2
800.6.q	\(\chi_{800}(249, \cdot)\)	None	0	2
800.6.s	\(\chi_{800}(7, \cdot)\)	None	0	2
800.6.u	\(\chi_{800}(161, \cdot)\)	n/a	600	4
800.6.v	\(\chi_{800}(43, \cdot)\)	n/a	1432	4
800.6.y	\(\chi_{800}(101, \cdot)\)	n/a	1508	4
800.6.ba	\(\chi_{800}(149, \cdot)\)	n/a	1432	4
800.6.bb	\(\chi_{800}(107, \cdot)\)	n/a	1432	4
800.6.be	\(\chi_{800}(209, \cdot)\)	n/a	592	4
800.6.bg	\(\chi_{800}(129, \cdot)\)	n/a	600	4
800.6.bj	\(\chi_{800}(81, \cdot)\)	n/a	592	4
800.6.bl	\(\chi_{800}(23, \cdot)\)	None	0	8
800.6.bm	\(\chi_{800}(41, \cdot)\)	None	0	8
800.6.bp	\(\chi_{800}(47, \cdot)\)	n/a	1184	8
800.6.bq	\(\chi_{800}(63, \cdot)\)	n/a	1200	8
800.6.bt	\(\chi_{800}(9, \cdot)\)	None	0	8
800.6.bu	\(\chi_{800}(87, \cdot)\)	None	0	8
800.6.bx	\(\chi_{800}(67, \cdot)\)	n/a	9568	16
800.6.by	\(\chi_{800}(29, \cdot)\)	n/a	9568	16
800.6.ca	\(\chi_{800}(21, \cdot)\)	n/a	9568	16
800.6.cd	\(\chi_{800}(3, \cdot)\)	n/a	9568	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(800))\) into lower level spaces

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