Space of modular forms of level 539 and weight 8

• Label: 539.8
• Level: 539
• Weight: 8
• Dimension: 77242
• Nonzero newspaces: 16
• Sturm bound: 188160
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(188160\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(539))\).

	Total	New	Old
Modular forms	82920	78114	4806
Cusp forms	81720	77242	4478
Eisenstein series	1200	872	328

Trace form

77242 * q - 125 * q^2 - 17 * q^3 - 1149 * q^4 - 137 * q^5 + 6767 * q^6 + 520 * q^7 - 12009 * q^8 + 129 * q^9 - 26478 * q^10 + 5657 * q^11 + 64572 * q^12 - 31958 * q^13 + 92808 * q^14 + 40047 * q^15 - 296737 * q^16 - 307220 * q^17 - 370228 * q^18 + 180380 * q^19 + 1642970 * q^20 + 283614 * q^21 - 217838 * q^22 - 1015447 * q^23 - 1807911 * q^24 - 432435 * q^25 + 592288 * q^26 + 1656361 * q^27 + 1175680 * q^28 + 703326 * q^29 - 2967932 * q^30 - 2297277 * q^31 + 1341068 * q^32 + 1713360 * q^33 + 1953344 * q^34 - 203334 * q^35 + 1874944 * q^36 - 292183 * q^37 - 10788852 * q^38 - 12034386 * q^39 - 682148 * q^40 + 10379386 * q^41 + 14061714 * q^42 + 8263650 * q^43 + 15154707 * q^44 + 10822204 * q^45 - 16684338 * q^46 - 22469572 * q^47 - 67539374 * q^48 - 22267628 * q^49 - 10020943 * q^50 + 1646026 * q^51 + 39890774 * q^52 + 32928660 * q^53 + 71282850 * q^54 + 17934995 * q^55 + 25583520 * q^56 + 16526130 * q^57 - 6090284 * q^58 - 23010871 * q^59 - 87099760 * q^60 - 18980176 * q^61 - 49052834 * q^62 - 19013574 * q^63 - 39777213 * q^64 - 10500824 * q^65 + 47487823 * q^66 + 48353655 * q^67 + 119722610 * q^68 + 150708665 * q^69 + 82506186 * q^70 + 23605797 * q^71 - 16423049 * q^72 - 28425882 * q^73 - 132310698 * q^74 - 180518768 * q^75 - 227995266 * q^76 - 46116909 * q^77 - 197927266 * q^78 - 90417134 * q^79 + 92840078 * q^80 + 78296730 * q^81 + 8261123 * q^82 + 69835146 * q^83 + 28005696 * q^84 + 214706330 * q^85 + 180720177 * q^86 + 171480384 * q^87 + 142756761 * q^88 + 62646471 * q^89 + 40513380 * q^90 - 37046596 * q^91 - 341340044 * q^92 - 268337523 * q^93 - 98007472 * q^94 - 16358796 * q^95 - 304830462 * q^96 - 81183245 * q^97 - 401433324 * q^98 - 95572085 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(539))\)

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
539.8.a	\(\chi_{539}(1, \cdot)\)	539.8.a.a	2	1
		539.8.a.b	4
		539.8.a.c	7
		539.8.a.d	9
		539.8.a.e	9
		539.8.a.f	11
		539.8.a.g	16
		539.8.a.h	20
		539.8.a.i	23
		539.8.a.j	23
		539.8.a.k	23
		539.8.a.l	23
		539.8.a.m	30
		539.8.a.n	38
539.8.b	\(\chi_{539}(538, \cdot)\)	n/a	276	1
539.8.e	\(\chi_{539}(67, \cdot)\)	n/a	468	2
539.8.f	\(\chi_{539}(148, \cdot)\)	n/a	1128	4
539.8.i	\(\chi_{539}(362, \cdot)\)	n/a	552	2
539.8.j	\(\chi_{539}(78, \cdot)\)	n/a	1968	6
539.8.m	\(\chi_{539}(195, \cdot)\)	n/a	1104	4
539.8.p	\(\chi_{539}(76, \cdot)\)	n/a	2340	6
539.8.q	\(\chi_{539}(214, \cdot)\)	n/a	2208	8
539.8.r	\(\chi_{539}(23, \cdot)\)	n/a	3912	12
539.8.s	\(\chi_{539}(19, \cdot)\)	n/a	2208	8
539.8.v	\(\chi_{539}(15, \cdot)\)	n/a	9360	24
539.8.w	\(\chi_{539}(10, \cdot)\)	n/a	4680	12
539.8.z	\(\chi_{539}(6, \cdot)\)	n/a	9360	24
539.8.bc	\(\chi_{539}(4, \cdot)\)	n/a	18720	48
539.8.bf	\(\chi_{539}(17, \cdot)\)	n/a	18720	48

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(539))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(539)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)