Space of modular forms of level 525 and weight 8

• Label: 525.8
• Level: 525
• Weight: 8
• Dimension: 44312
• Nonzero newspaces: 24
• Sturm bound: 153600
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(153600\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(525))\).

	Total	New	Old
Modular forms	67872	44724	23148
Cusp forms	66528	44312	22216
Eisenstein series	1344	412	932

Trace form

44312 * q - 76 * q^2 + 104 * q^3 - 878 * q^4 - 108 * q^5 + 3132 * q^6 + 6302 * q^7 - 14010 * q^8 - 8842 * q^9 - 4608 * q^10 + 23618 * q^11 + 27104 * q^12 - 17398 * q^13 - 109416 * q^14 + 32492 * q^15 + 9154 * q^16 + 359512 * q^17 - 339694 * q^18 - 617594 * q^19 - 1224312 * q^20 + 118470 * q^21 + 1138392 * q^22 + 1635736 * q^23 + 468444 * q^24 + 1273652 * q^25 + 272730 * q^26 - 243358 * q^27 - 4650714 * q^28 - 1454056 * q^29 - 1957108 * q^30 - 1236666 * q^31 + 5271518 * q^32 + 3425774 * q^33 + 13511732 * q^34 + 2064668 * q^35 + 4079510 * q^36 - 9857016 * q^37 - 9327442 * q^38 - 2120286 * q^39 - 1650704 * q^40 - 3822172 * q^41 + 733848 * q^42 + 1766456 * q^43 - 1252608 * q^44 - 435932 * q^45 + 18370244 * q^46 + 7012078 * q^47 + 20046940 * q^48 - 41590 * q^49 + 28529368 * q^50 - 6461476 * q^51 - 22279344 * q^52 - 8147392 * q^53 - 41998002 * q^54 - 32075032 * q^55 + 16670298 * q^56 + 17956144 * q^57 + 48214496 * q^58 + 24998476 * q^59 + 49773764 * q^60 - 6677726 * q^61 - 2387396 * q^62 - 6260878 * q^63 - 87614202 * q^64 - 52038868 * q^65 - 77882190 * q^66 - 38935878 * q^67 + 75815344 * q^68 + 60091996 * q^69 + 111358244 * q^70 + 73453900 * q^71 + 83253582 * q^72 + 28090856 * q^73 + 397174 * q^74 - 56222556 * q^75 - 111060024 * q^76 - 132339840 * q^77 - 170225744 * q^78 - 197900354 * q^79 - 87533248 * q^80 - 33993502 * q^81 - 72363048 * q^82 + 118042364 * q^83 + 248842690 * q^84 + 287414556 * q^85 + 98500214 * q^86 + 90197352 * q^87 + 188252812 * q^88 - 1449228 * q^89 - 142758604 * q^90 + 22145892 * q^91 - 226694032 * q^92 - 169961288 * q^93 - 469102168 * q^94 - 39923632 * q^95 - 119479308 * q^96 + 46830300 * q^97 + 155792814 * q^98 + 12604692 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(525))\)

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
525.8.a	\(\chi_{525}(1, \cdot)\)	525.8.a.a	1	1
		525.8.a.b	1
		525.8.a.c	1
		525.8.a.d	2
		525.8.a.e	2
		525.8.a.f	2
		525.8.a.g	3
		525.8.a.h	4
		525.8.a.i	4
		525.8.a.j	4
		525.8.a.k	4
		525.8.a.l	4
		525.8.a.m	4
		525.8.a.n	6
		525.8.a.o	6
		525.8.a.p	6
		525.8.a.q	6
		525.8.a.r	8
		525.8.a.s	8
		525.8.a.t	8
		525.8.a.u	8
		525.8.a.v	9
		525.8.a.w	9
		525.8.a.x	11
		525.8.a.y	11
525.8.b	\(\chi_{525}(251, \cdot)\)	n/a	348	1
525.8.d	\(\chi_{525}(274, \cdot)\)	n/a	128	1
525.8.g	\(\chi_{525}(524, \cdot)\)	n/a	332	1
525.8.i	\(\chi_{525}(151, \cdot)\)	n/a	354	2
525.8.j	\(\chi_{525}(218, \cdot)\)	n/a	504	2
525.8.m	\(\chi_{525}(118, \cdot)\)	n/a	336	2
525.8.n	\(\chi_{525}(106, \cdot)\)	n/a	848	4
525.8.q	\(\chi_{525}(299, \cdot)\)	n/a	664	2
525.8.r	\(\chi_{525}(424, \cdot)\)	n/a	336	2
525.8.t	\(\chi_{525}(26, \cdot)\)	n/a	698	2
525.8.w	\(\chi_{525}(104, \cdot)\)	n/a	2224	4
525.8.z	\(\chi_{525}(64, \cdot)\)	n/a	832	4
525.8.bb	\(\chi_{525}(41, \cdot)\)	n/a	2224	4
525.8.bc	\(\chi_{525}(82, \cdot)\)	n/a	672	4
525.8.bf	\(\chi_{525}(32, \cdot)\)	n/a	1328	4
525.8.bg	\(\chi_{525}(16, \cdot)\)	n/a	2240	8
525.8.bh	\(\chi_{525}(13, \cdot)\)	n/a	2240	8
525.8.bk	\(\chi_{525}(8, \cdot)\)	n/a	3360	8
525.8.bm	\(\chi_{525}(131, \cdot)\)	n/a	4448	8
525.8.bo	\(\chi_{525}(4, \cdot)\)	n/a	2240	8
525.8.bp	\(\chi_{525}(59, \cdot)\)	n/a	4448	8
525.8.bs	\(\chi_{525}(2, \cdot)\)	n/a	8896	16
525.8.bv	\(\chi_{525}(52, \cdot)\)	n/a	4480	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(525))\) into lower level spaces

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