Space of modular forms of level 160 and weight 8

• Label: 160.8
• Level: 160
• Weight: 8
• Dimension: 2742
• Nonzero newspaces: 10
• Sturm bound: 12288
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(12288\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(160))\).

	Total	New	Old
Modular forms	5504	2802	2702
Cusp forms	5248	2742	2506
Eisenstein series	256	60	196

Trace form

2742 * q - 8 * q^2 - 4 * q^3 - 8 * q^4 + 266 * q^5 - 24 * q^6 - 1380 * q^7 - 8 * q^8 + 86 * q^9 + 12988 * q^10 - 16 * q^11 - 61352 * q^12 - 27244 * q^13 + 52376 * q^14 + 17860 * q^15 + 105536 * q^16 - 59580 * q^17 - 204128 * q^18 - 8 * q^19 - 82012 * q^20 + 50152 * q^21 + 748464 * q^22 + 284236 * q^23 - 761776 * q^24 - 36630 * q^25 + 727936 * q^26 - 960928 * q^27 + 390912 * q^28 + 135196 * q^29 - 870484 * q^30 + 1787448 * q^31 - 1071328 * q^32 - 584680 * q^33 + 402128 * q^34 - 1633016 * q^35 + 3339392 * q^36 + 1681900 * q^37 + 5066184 * q^38 + 1809680 * q^39 - 2746360 * q^40 - 1013612 * q^41 - 9849888 * q^42 - 2238068 * q^43 + 3170792 * q^44 - 2952226 * q^45 + 5431592 * q^46 + 2076444 * q^47 + 10088720 * q^48 + 4511534 * q^49 + 1653788 * q^50 - 3010840 * q^51 - 17764440 * q^52 - 7486132 * q^53 - 13631568 * q^54 + 608244 * q^55 + 7309968 * q^56 + 912152 * q^57 + 24897456 * q^58 + 3671864 * q^59 + 6626936 * q^60 + 12496868 * q^61 - 25897216 * q^62 - 5164700 * q^63 - 11843216 * q^64 - 2852364 * q^65 - 37518520 * q^66 - 5306876 * q^67 - 553088 * q^68 - 29700776 * q^69 + 47532168 * q^70 + 21851888 * q^71 + 71223736 * q^72 - 5494996 * q^73 + 13434088 * q^74 - 9792144 * q^75 - 48998808 * q^76 + 24365240 * q^77 - 56780136 * q^78 + 12310256 * q^79 - 64506664 * q^80 + 4991414 * q^81 - 66974888 * q^82 + 18628276 * q^83 + 50317600 * q^84 + 20885452 * q^85 + 109445088 * q^86 - 115705416 * q^87 + 116468576 * q^88 - 3811892 * q^89 + 74995224 * q^90 + 5288112 * q^91 - 128197136 * q^92 - 25950864 * q^93 - 117718160 * q^94 + 70760816 * q^95 - 59497120 * q^96 + 90049204 * q^97 + 31187600 * q^98 + 19476944 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.8.a	\(\chi_{160}(1, \cdot)\)	160.8.a.a	2	1
		160.8.a.b	2
		160.8.a.c	2
		160.8.a.d	2
		160.8.a.e	2
		160.8.a.f	3
		160.8.a.g	3
		160.8.a.h	4
		160.8.a.i	4
		160.8.a.j	4
160.8.c	\(\chi_{160}(129, \cdot)\)	160.8.c.a	2	1
		160.8.c.b	4
		160.8.c.c	16
		160.8.c.d	20
160.8.d	\(\chi_{160}(81, \cdot)\)	160.8.d.a	28	1
160.8.f	\(\chi_{160}(49, \cdot)\)	160.8.f.a	40	1
160.8.j	\(\chi_{160}(87, \cdot)\)	None	0	2
160.8.l	\(\chi_{160}(41, \cdot)\)	None	0	2
160.8.n	\(\chi_{160}(63, \cdot)\)	160.8.n.a	20	2
		160.8.n.b	20
		160.8.n.c	22
		160.8.n.d	22
160.8.o	\(\chi_{160}(47, \cdot)\)	160.8.o.a	80	2
160.8.q	\(\chi_{160}(9, \cdot)\)	None	0	2
160.8.s	\(\chi_{160}(7, \cdot)\)	None	0	2
160.8.u	\(\chi_{160}(43, \cdot)\)	n/a	664	4
160.8.x	\(\chi_{160}(21, \cdot)\)	n/a	448	4
160.8.z	\(\chi_{160}(29, \cdot)\)	n/a	664	4
160.8.ba	\(\chi_{160}(3, \cdot)\)	n/a	664	4

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(160)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)