Space of modular forms of level 825 and weight 6

• Label: 825.6
• Level: 825
• Weight: 6
• Dimension: 81198
• Nonzero newspaces: 42
• Sturm bound: 288000
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(288000\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(825))\).

	Total	New	Old
Modular forms	121120	81938	39182
Cusp forms	118880	81198	37682
Eisenstein series	2240	740	1500

Trace form

81198 * q - 20 * q^2 - 63 * q^3 + 286 * q^4 + 252 * q^5 - 997 * q^6 - 2168 * q^7 - 224 * q^8 + 991 * q^9 + 3408 * q^10 + 1534 * q^11 - 1350 * q^12 - 8888 * q^13 - 21474 * q^14 - 6852 * q^15 - 20738 * q^16 + 4766 * q^17 + 32825 * q^18 + 49668 * q^19 + 47688 * q^20 + 15500 * q^21 + 9406 * q^22 - 35484 * q^23 - 45091 * q^24 - 65948 * q^25 - 79514 * q^26 - 43278 * q^27 - 21136 * q^28 + 92216 * q^29 + 42732 * q^30 - 7350 * q^31 + 124772 * q^32 - 14267 * q^33 - 116188 * q^34 - 83800 * q^35 + 231307 * q^36 + 92702 * q^37 - 69538 * q^38 + 123500 * q^39 + 268976 * q^40 + 139480 * q^41 - 86284 * q^42 - 39276 * q^43 + 422322 * q^44 - 80448 * q^45 + 233320 * q^46 + 108718 * q^47 - 120554 * q^48 - 339046 * q^49 - 716952 * q^50 + 20514 * q^51 - 764344 * q^52 - 492654 * q^53 - 16456 * q^54 - 240964 * q^55 - 922760 * q^56 - 17078 * q^57 - 147316 * q^58 + 207542 * q^59 + 837852 * q^60 + 361584 * q^61 + 794584 * q^62 - 161468 * q^63 + 2236302 * q^64 + 454636 * q^65 + 244274 * q^66 + 383566 * q^67 - 131760 * q^68 - 127009 * q^69 - 925480 * q^70 - 135604 * q^71 + 323146 * q^72 - 808464 * q^73 - 793114 * q^74 + 329908 * q^75 - 888112 * q^76 - 131898 * q^77 + 1703564 * q^78 + 645360 * q^79 + 329368 * q^80 + 965823 * q^81 - 1433406 * q^82 - 581670 * q^83 - 1275236 * q^84 + 1138644 * q^85 + 1319168 * q^86 - 161076 * q^87 + 1869618 * q^88 + 1133848 * q^89 - 645072 * q^90 - 3605820 * q^91 - 3603558 * q^92 - 95837 * q^93 - 755040 * q^94 + 101168 * q^95 + 5555740 * q^96 + 1565726 * q^97 + 3754768 * q^98 + 2783065 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(825))\)

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
825.6.a	\(\chi_{825}(1, \cdot)\)	825.6.a.a	1	1
		825.6.a.b	1
		825.6.a.c	2
		825.6.a.d	2
		825.6.a.e	2
		825.6.a.f	3
		825.6.a.g	3
		825.6.a.h	3
		825.6.a.i	3
		825.6.a.j	3
		825.6.a.k	5
		825.6.a.l	5
		825.6.a.m	7
		825.6.a.n	7
		825.6.a.o	7
		825.6.a.p	8
		825.6.a.q	8
		825.6.a.r	9
		825.6.a.s	9
		825.6.a.t	10
		825.6.a.u	10
		825.6.a.v	13
		825.6.a.w	13
		825.6.a.x	13
		825.6.a.y	13
825.6.c	\(\chi_{825}(199, \cdot)\)	n/a	148	1
825.6.d	\(\chi_{825}(824, \cdot)\)	n/a	356	1
825.6.f	\(\chi_{825}(626, \cdot)\)	n/a	374	1
825.6.j	\(\chi_{825}(43, \cdot)\)	n/a	360	2
825.6.k	\(\chi_{825}(518, \cdot)\)	n/a	600	2
825.6.m	\(\chi_{825}(16, \cdot)\)	n/a	1200	4
825.6.n	\(\chi_{825}(301, \cdot)\)	n/a	760	4
825.6.o	\(\chi_{825}(421, \cdot)\)	n/a	1200	4
825.6.p	\(\chi_{825}(181, \cdot)\)	n/a	1200	4
825.6.q	\(\chi_{825}(166, \cdot)\)	n/a	992	4
825.6.r	\(\chi_{825}(31, \cdot)\)	n/a	1200	4
825.6.s	\(\chi_{825}(479, \cdot)\)	n/a	2384	4
825.6.v	\(\chi_{825}(379, \cdot)\)	n/a	1200	4
825.6.x	\(\chi_{825}(131, \cdot)\)	n/a	2384	4
825.6.bd	\(\chi_{825}(281, \cdot)\)	n/a	2384	4
825.6.bf	\(\chi_{825}(266, \cdot)\)	n/a	2384	4
825.6.bi	\(\chi_{825}(101, \cdot)\)	n/a	1496	4
825.6.bj	\(\chi_{825}(116, \cdot)\)	n/a	2384	4
825.6.bl	\(\chi_{825}(34, \cdot)\)	n/a	1008	4
825.6.bo	\(\chi_{825}(134, \cdot)\)	n/a	2384	4
825.6.br	\(\chi_{825}(29, \cdot)\)	n/a	2384	4
825.6.bs	\(\chi_{825}(74, \cdot)\)	n/a	1424	4
825.6.bu	\(\chi_{825}(239, \cdot)\)	n/a	2384	4
825.6.bv	\(\chi_{825}(229, \cdot)\)	n/a	1200	4
825.6.bx	\(\chi_{825}(49, \cdot)\)	n/a	720	4
825.6.by	\(\chi_{825}(4, \cdot)\)	n/a	1200	4
825.6.cb	\(\chi_{825}(169, \cdot)\)	n/a	1200	4
825.6.ce	\(\chi_{825}(164, \cdot)\)	n/a	2384	4
825.6.cg	\(\chi_{825}(41, \cdot)\)	n/a	2384	4
825.6.ci	\(\chi_{825}(113, \cdot)\)	n/a	4768	8
825.6.cl	\(\chi_{825}(28, \cdot)\)	n/a	2400	8
825.6.cm	\(\chi_{825}(13, \cdot)\)	n/a	2400	8
825.6.cs	\(\chi_{825}(23, \cdot)\)	n/a	4000	8
825.6.ct	\(\chi_{825}(218, \cdot)\)	n/a	2848	8
825.6.cu	\(\chi_{825}(53, \cdot)\)	n/a	4768	8
825.6.cv	\(\chi_{825}(38, \cdot)\)	n/a	4768	8
825.6.cw	\(\chi_{825}(7, \cdot)\)	n/a	1440	8
825.6.cx	\(\chi_{825}(52, \cdot)\)	n/a	2400	8
825.6.cy	\(\chi_{825}(172, \cdot)\)	n/a	2400	8
825.6.cz	\(\chi_{825}(142, \cdot)\)	n/a	2400	8
825.6.df	\(\chi_{825}(47, \cdot)\)	n/a	4768	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(825))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(825)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)