Space of modular forms of level 825 and weight 4

• Label: 825.4
• Level: 825
• Weight: 4
• Dimension: 48572
• Nonzero newspaces: 42
• Sturm bound: 192000
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(192000\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(825))\).

	Total	New	Old
Modular forms	73120	49312	23808
Cusp forms	70880	48572	22308
Eisenstein series	2240	740	1500

Trace form

48572 * q + 16 * q^2 - 69 * q^3 - 186 * q^4 + 12 * q^5 - 19 * q^6 - 150 * q^7 - 224 * q^8 - 197 * q^9 - 312 * q^10 - 212 * q^11 + 162 * q^12 + 526 * q^13 + 1446 * q^14 + 288 * q^15 + 814 * q^16 - 820 * q^17 - 1081 * q^18 - 2044 * q^19 - 312 * q^20 - 2356 * q^21 - 970 * q^22 + 228 * q^23 + 653 * q^24 + 2932 * q^25 + 2638 * q^26 + 2793 * q^27 + 6624 * q^28 + 4172 * q^29 + 1692 * q^30 + 2330 * q^31 - 2236 * q^32 + 766 * q^33 - 7212 * q^34 - 4480 * q^35 - 2657 * q^36 - 7310 * q^37 - 12178 * q^38 - 8491 * q^39 - 11184 * q^40 - 5516 * q^41 - 10888 * q^42 - 9792 * q^43 - 14574 * q^44 + 4752 * q^45 + 2760 * q^46 + 6148 * q^47 + 10990 * q^48 + 16910 * q^49 + 21888 * q^50 + 9390 * q^51 + 43976 * q^52 + 19908 * q^53 + 10376 * q^54 + 9996 * q^55 + 35320 * q^56 + 11344 * q^57 + 18884 * q^58 + 2564 * q^59 + 3612 * q^60 + 2686 * q^61 - 18032 * q^62 + 3373 * q^63 - 31554 * q^64 - 9164 * q^65 - 4678 * q^66 - 20864 * q^67 - 35472 * q^68 - 14794 * q^69 - 18120 * q^70 - 892 * q^71 - 27686 * q^72 - 6550 * q^73 - 11554 * q^74 - 18872 * q^75 - 22016 * q^76 - 4356 * q^77 - 24220 * q^78 - 9770 * q^79 + 2008 * q^80 - 7353 * q^81 - 30322 * q^82 - 29928 * q^83 - 22916 * q^84 - 25236 * q^85 - 8344 * q^86 - 9204 * q^87 - 14942 * q^88 - 10304 * q^89 + 7128 * q^90 - 20210 * q^91 - 46326 * q^92 - 6239 * q^93 - 2576 * q^94 + 15728 * q^95 + 3460 * q^96 + 45336 * q^97 + 40756 * q^98 + 6421 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(825))\)

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
825.4.a	\(\chi_{825}(1, \cdot)\)	825.4.a.a	1	1
		825.4.a.b	1
		825.4.a.c	1
		825.4.a.d	1
		825.4.a.e	1
		825.4.a.f	1
		825.4.a.g	1
		825.4.a.h	1
		825.4.a.i	1
		825.4.a.j	1
		825.4.a.k	2
		825.4.a.l	2
		825.4.a.m	2
		825.4.a.n	3
		825.4.a.o	3
		825.4.a.p	3
		825.4.a.q	3
		825.4.a.r	3
		825.4.a.s	3
		825.4.a.t	4
		825.4.a.u	4
		825.4.a.v	4
		825.4.a.w	5
		825.4.a.x	5
		825.4.a.y	5
		825.4.a.z	5
		825.4.a.ba	7
		825.4.a.bb	7
		825.4.a.bc	7
		825.4.a.bd	7
825.4.c	\(\chi_{825}(199, \cdot)\)	825.4.c.a	2	1
		825.4.c.b	2
		825.4.c.c	2
		825.4.c.d	2
		825.4.c.e	2
		825.4.c.f	2
		825.4.c.g	2
		825.4.c.h	4
		825.4.c.i	4
		825.4.c.j	4
		825.4.c.k	6
		825.4.c.l	6
		825.4.c.m	6
		825.4.c.n	6
		825.4.c.o	6
		825.4.c.p	8
		825.4.c.q	8
		825.4.c.r	10
		825.4.c.s	10
825.4.d	\(\chi_{825}(824, \cdot)\)	n/a	212	1
825.4.f	\(\chi_{825}(626, \cdot)\)	n/a	222	1
825.4.j	\(\chi_{825}(43, \cdot)\)	n/a	216	2
825.4.k	\(\chi_{825}(518, \cdot)\)	n/a	360	2
825.4.m	\(\chi_{825}(16, \cdot)\)	n/a	720	4
825.4.n	\(\chi_{825}(301, \cdot)\)	n/a	456	4
825.4.o	\(\chi_{825}(421, \cdot)\)	n/a	720	4
825.4.p	\(\chi_{825}(181, \cdot)\)	n/a	720	4
825.4.q	\(\chi_{825}(166, \cdot)\)	n/a	608	4
825.4.r	\(\chi_{825}(31, \cdot)\)	n/a	720	4
825.4.s	\(\chi_{825}(479, \cdot)\)	n/a	1424	4
825.4.v	\(\chi_{825}(379, \cdot)\)	n/a	720	4
825.4.x	\(\chi_{825}(131, \cdot)\)	n/a	1424	4
825.4.bd	\(\chi_{825}(281, \cdot)\)	n/a	1424	4
825.4.bf	\(\chi_{825}(266, \cdot)\)	n/a	1424	4
825.4.bi	\(\chi_{825}(101, \cdot)\)	n/a	888	4
825.4.bj	\(\chi_{825}(116, \cdot)\)	n/a	1424	4
825.4.bl	\(\chi_{825}(34, \cdot)\)	n/a	592	4
825.4.bo	\(\chi_{825}(134, \cdot)\)	n/a	1424	4
825.4.br	\(\chi_{825}(29, \cdot)\)	n/a	1424	4
825.4.bs	\(\chi_{825}(74, \cdot)\)	n/a	848	4
825.4.bu	\(\chi_{825}(239, \cdot)\)	n/a	1424	4
825.4.bv	\(\chi_{825}(229, \cdot)\)	n/a	720	4
825.4.bx	\(\chi_{825}(49, \cdot)\)	n/a	432	4
825.4.by	\(\chi_{825}(4, \cdot)\)	n/a	720	4
825.4.cb	\(\chi_{825}(169, \cdot)\)	n/a	720	4
825.4.ce	\(\chi_{825}(164, \cdot)\)	n/a	1424	4
825.4.cg	\(\chi_{825}(41, \cdot)\)	n/a	1424	4
825.4.ci	\(\chi_{825}(113, \cdot)\)	n/a	2848	8
825.4.cl	\(\chi_{825}(28, \cdot)\)	n/a	1440	8
825.4.cm	\(\chi_{825}(13, \cdot)\)	n/a	1440	8
825.4.cs	\(\chi_{825}(23, \cdot)\)	n/a	2400	8
825.4.ct	\(\chi_{825}(218, \cdot)\)	n/a	1696	8
825.4.cu	\(\chi_{825}(53, \cdot)\)	n/a	2848	8
825.4.cv	\(\chi_{825}(38, \cdot)\)	n/a	2848	8
825.4.cw	\(\chi_{825}(7, \cdot)\)	n/a	864	8
825.4.cx	\(\chi_{825}(52, \cdot)\)	n/a	1440	8
825.4.cy	\(\chi_{825}(172, \cdot)\)	n/a	1440	8
825.4.cz	\(\chi_{825}(142, \cdot)\)	n/a	1440	8
825.4.df	\(\chi_{825}(47, \cdot)\)	n/a	2848	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(825))\) into lower level spaces

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