Space of modular forms of level 320 and weight 8

• Label: 320.8
• Level: 320
• Weight: 8
• Dimension: 11022
• Nonzero newspaces: 14
• Sturm bound: 49152
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(49152\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(320))\).

	Total	New	Old
Modular forms	21792	11154	10638
Cusp forms	21216	11022	10194
Eisenstein series	576	132	444

Trace form

11022 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 24 * q^5 - 48 * q^6 - 8 * q^7 - 16 * q^8 + 4354 * q^9 - 24 * q^10 + 2372 * q^11 - 16 * q^12 + 14112 * q^13 - 16 * q^14 - 27020 * q^15 - 48 * q^16 + 11604 * q^17 - 16 * q^18 + 121156 * q^19 - 24 * q^20 - 72408 * q^21 - 548928 * q^22 - 8 * q^23 + 1196064 * q^24 - 64526 * q^25 - 1455968 * q^26 - 467352 * q^27 - 781856 * q^28 + 206736 * q^29 + 1739896 * q^30 + 714928 * q^31 + 2142624 * q^32 + 800864 * q^33 - 806336 * q^34 - 252020 * q^35 - 8139088 * q^36 - 2930368 * q^37 - 2489856 * q^38 - 16 * q^39 + 2686336 * q^40 + 5935044 * q^41 + 7717824 * q^42 + 1139500 * q^43 - 6740960 * q^44 - 1417988 * q^45 - 48 * q^46 - 4152936 * q^47 - 16 * q^48 - 3691306 * q^49 + 2317392 * q^50 + 17192296 * q^51 - 20409904 * q^52 + 7731968 * q^53 + 2519408 * q^54 - 8382032 * q^55 + 21474496 * q^56 - 8958528 * q^57 + 20716256 * q^58 - 17074036 * q^59 - 4336440 * q^60 - 614912 * q^61 - 20697072 * q^62 + 50009400 * q^63 - 45674320 * q^64 + 9290496 * q^65 - 15030512 * q^66 - 515180 * q^67 + 17500112 * q^68 - 3765880 * q^69 + 35990280 * q^70 - 74092256 * q^71 + 45454592 * q^72 - 15809492 * q^73 - 8428800 * q^74 + 25953072 * q^75 - 77885872 * q^76 + 8787624 * q^77 - 137665792 * q^78 + 21292784 * q^79 + 78362432 * q^80 + 68845414 * q^81 + 98629264 * q^82 + 10069348 * q^83 - 34113648 * q^84 - 46915856 * q^85 - 139071136 * q^86 - 81578232 * q^87 - 105035696 * q^88 - 80039796 * q^89 - 31734024 * q^90 + 8226984 * q^91 + 108881536 * q^92 + 123704768 * q^93 + 149383088 * q^94 + 59772588 * q^95 + 225737920 * q^96 + 50868964 * q^97 + 125538048 * q^98 - 668740 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.8.a	\(\chi_{320}(1, \cdot)\)	320.8.a.a	1	1
		320.8.a.b	1
		320.8.a.c	1
		320.8.a.d	1
		320.8.a.e	1
		320.8.a.f	1
		320.8.a.g	1
		320.8.a.h	1
		320.8.a.i	2
		320.8.a.j	2
		320.8.a.k	2
		320.8.a.l	2
		320.8.a.m	2
		320.8.a.n	2
		320.8.a.o	2
		320.8.a.p	2
		320.8.a.q	2
		320.8.a.r	2
		320.8.a.s	2
		320.8.a.t	2
		320.8.a.u	2
		320.8.a.v	2
		320.8.a.w	2
		320.8.a.x	3
		320.8.a.y	3
		320.8.a.z	4
		320.8.a.ba	4
		320.8.a.bb	4
320.8.c	\(\chi_{320}(129, \cdot)\)	320.8.c.a	2	1
		320.8.c.b	2
		320.8.c.c	2
		320.8.c.d	2
		320.8.c.e	2
		320.8.c.f	4
		320.8.c.g	4
		320.8.c.h	4
		320.8.c.i	4
		320.8.c.j	4
		320.8.c.k	8
		320.8.c.l	8
		320.8.c.m	16
		320.8.c.n	20
320.8.d	\(\chi_{320}(161, \cdot)\)	320.8.d.a	8	1
		320.8.d.b	8
		320.8.d.c	20
		320.8.d.d	20
320.8.f	\(\chi_{320}(289, \cdot)\)	320.8.f.a	4	1
		320.8.f.b	24
		320.8.f.c	56
320.8.j	\(\chi_{320}(47, \cdot)\)	n/a	164	2
320.8.l	\(\chi_{320}(81, \cdot)\)	n/a	112	2
320.8.n	\(\chi_{320}(63, \cdot)\)	n/a	164	2
320.8.o	\(\chi_{320}(223, \cdot)\)	n/a	168	2
320.8.q	\(\chi_{320}(49, \cdot)\)	n/a	164	2
320.8.s	\(\chi_{320}(207, \cdot)\)	n/a	164	2
320.8.u	\(\chi_{320}(87, \cdot)\)	None	0	4
320.8.x	\(\chi_{320}(41, \cdot)\)	None	0	4
320.8.z	\(\chi_{320}(9, \cdot)\)	None	0	4
320.8.ba	\(\chi_{320}(7, \cdot)\)	None	0	4
320.8.bd	\(\chi_{320}(43, \cdot)\)	n/a	2672	8
320.8.be	\(\chi_{320}(21, \cdot)\)	n/a	1792	8
320.8.bf	\(\chi_{320}(29, \cdot)\)	n/a	2672	8
320.8.bj	\(\chi_{320}(3, \cdot)\)	n/a	2672	8

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(320)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)