Space of modular forms of level 525 and weight 4

• Label: 525.4
• Level: 525
• Weight: 4
• Dimension: 18874
• Nonzero newspaces: 24
• Sturm bound: 76800
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(76800\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(525))\).

	Total	New	Old
Modular forms	29472	19286	10186
Cusp forms	28128	18874	9254
Eisenstein series	1344	412	932

Trace form

18874 * q + 16 * q^2 - 37 * q^3 - 134 * q^4 + 12 * q^5 - 60 * q^6 - 146 * q^7 - 90 * q^8 - 49 * q^9 - 248 * q^10 - 224 * q^11 + 320 * q^12 + 540 * q^13 + 216 * q^14 + 272 * q^15 + 18 * q^16 - 1132 * q^17 - 922 * q^18 - 978 * q^19 - 312 * q^20 - 393 * q^21 + 1128 * q^22 + 440 * q^23 + 300 * q^24 + 1652 * q^25 - 1254 * q^26 + 1100 * q^27 + 134 * q^28 + 3208 * q^29 + 2732 * q^30 + 2402 * q^31 + 2830 * q^32 + 1055 * q^33 - 2700 * q^34 + 208 * q^35 + 2510 * q^36 - 1758 * q^37 - 5594 * q^38 - 4500 * q^39 - 7984 * q^40 - 3872 * q^41 - 996 * q^42 + 328 * q^43 - 336 * q^44 + 2128 * q^45 + 1700 * q^46 + 2744 * q^47 + 3004 * q^48 + 234 * q^49 + 16448 * q^50 + 731 * q^51 + 7952 * q^52 + 5008 * q^53 + 2502 * q^54 - 3832 * q^55 - 20166 * q^56 - 5690 * q^57 - 26912 * q^58 - 12784 * q^59 - 2716 * q^60 + 50 * q^61 - 12724 * q^62 + 3917 * q^63 + 12214 * q^64 + 4612 * q^65 + 18762 * q^66 + 25574 * q^67 + 34448 * q^68 + 5968 * q^69 + 23204 * q^70 + 9620 * q^71 - 22722 * q^72 + 5610 * q^73 + 9638 * q^74 - 15096 * q^75 - 7848 * q^76 + 108 * q^77 - 17192 * q^78 - 14686 * q^79 - 6848 * q^80 + 4499 * q^81 - 51776 * q^82 - 39704 * q^83 - 18326 * q^84 - 41684 * q^85 - 36194 * q^86 + 864 * q^87 - 33524 * q^88 - 8556 * q^89 + 31916 * q^90 + 8224 * q^91 + 16720 * q^92 + 30871 * q^93 + 58296 * q^94 + 31888 * q^95 + 16788 * q^96 + 62284 * q^97 + 19242 * q^98 - 14694 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(525))\)

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
525.4.a	\(\chi_{525}(1, \cdot)\)	525.4.a.a	1	1
		525.4.a.b	1
		525.4.a.c	1
		525.4.a.d	1
		525.4.a.e	1
		525.4.a.f	1
		525.4.a.g	1
		525.4.a.h	1
		525.4.a.i	2
		525.4.a.j	2
		525.4.a.k	2
		525.4.a.l	2
		525.4.a.m	2
		525.4.a.n	2
		525.4.a.o	2
		525.4.a.p	2
		525.4.a.q	3
		525.4.a.r	3
		525.4.a.s	4
		525.4.a.t	4
		525.4.a.u	4
		525.4.a.v	4
		525.4.a.w	5
		525.4.a.x	5
525.4.b	\(\chi_{525}(251, \cdot)\)	n/a	146	1
525.4.d	\(\chi_{525}(274, \cdot)\)	525.4.d.a	2	1
		525.4.d.b	2
		525.4.d.c	2
		525.4.d.d	2
		525.4.d.e	2
		525.4.d.f	2
		525.4.d.g	4
		525.4.d.h	4
		525.4.d.i	4
		525.4.d.j	4
		525.4.d.k	4
		525.4.d.l	4
		525.4.d.m	4
		525.4.d.n	8
		525.4.d.o	8
525.4.g	\(\chi_{525}(524, \cdot)\)	n/a	140	1
525.4.i	\(\chi_{525}(151, \cdot)\)	n/a	152	2
525.4.j	\(\chi_{525}(218, \cdot)\)	n/a	216	2
525.4.m	\(\chi_{525}(118, \cdot)\)	n/a	144	2
525.4.n	\(\chi_{525}(106, \cdot)\)	n/a	368	4
525.4.q	\(\chi_{525}(299, \cdot)\)	n/a	280	2
525.4.r	\(\chi_{525}(424, \cdot)\)	n/a	144	2
525.4.t	\(\chi_{525}(26, \cdot)\)	n/a	292	2
525.4.w	\(\chi_{525}(104, \cdot)\)	n/a	944	4
525.4.z	\(\chi_{525}(64, \cdot)\)	n/a	352	4
525.4.bb	\(\chi_{525}(41, \cdot)\)	n/a	944	4
525.4.bc	\(\chi_{525}(82, \cdot)\)	n/a	288	4
525.4.bf	\(\chi_{525}(32, \cdot)\)	n/a	560	4
525.4.bg	\(\chi_{525}(16, \cdot)\)	n/a	960	8
525.4.bh	\(\chi_{525}(13, \cdot)\)	n/a	960	8
525.4.bk	\(\chi_{525}(8, \cdot)\)	n/a	1440	8
525.4.bm	\(\chi_{525}(131, \cdot)\)	n/a	1888	8
525.4.bo	\(\chi_{525}(4, \cdot)\)	n/a	960	8
525.4.bp	\(\chi_{525}(59, \cdot)\)	n/a	1888	8
525.4.bs	\(\chi_{525}(2, \cdot)\)	n/a	3776	16
525.4.bv	\(\chi_{525}(52, \cdot)\)	n/a	1920	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(525))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(525)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)