Space of modular forms of level 320 and weight 5

• Label: 320.5
• Level: 320
• Weight: 5
• Dimension: 6270
• Nonzero newspaces: 14
• Sturm bound: 30720
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(30720\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(320))\).

	Total	New	Old
Modular forms	12576	6402	6174
Cusp forms	12000	6270	5730
Eisenstein series	576	132	444

Trace form

6270 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 24 * q^5 - 48 * q^6 - 16 * q^7 - 16 * q^8 - 182 * q^9 - 24 * q^10 + 156 * q^11 - 16 * q^12 + 688 * q^13 - 16 * q^14 - 16 * q^15 - 48 * q^16 - 988 * q^17 - 16 * q^18 - 1420 * q^19 - 24 * q^20 + 24 * q^21 + 5312 * q^22 + 2288 * q^23 + 544 * q^24 - 1374 * q^25 - 10848 * q^26 - 3336 * q^27 - 11296 * q^28 - 3472 * q^29 - 4744 * q^30 - 16 * q^31 + 5024 * q^32 + 7600 * q^33 + 14144 * q^34 + 1324 * q^35 + 37552 * q^36 + 3120 * q^37 + 15104 * q^38 + 5368 * q^39 - 384 * q^40 + 3012 * q^41 - 32576 * q^42 + 3380 * q^43 - 16864 * q^44 + 1604 * q^45 - 48 * q^46 - 8 * q^47 - 16 * q^48 - 1242 * q^49 - 21552 * q^50 + 26200 * q^51 - 17968 * q^52 - 20176 * q^53 + 31088 * q^54 - 35348 * q^55 + 49344 * q^56 - 19152 * q^57 + 65504 * q^58 - 57804 * q^59 + 31944 * q^60 + 16528 * q^61 + 12048 * q^62 + 19184 * q^63 - 24400 * q^64 + 27392 * q^65 - 71152 * q^66 + 97268 * q^67 - 53296 * q^68 - 17608 * q^69 - 61176 * q^70 + 79832 * q^71 - 81664 * q^72 - 6420 * q^73 - 33280 * q^74 - 39120 * q^75 + 28240 * q^76 + 4792 * q^77 + 207872 * q^78 - 100368 * q^79 + 115008 * q^80 + 37158 * q^81 + 10384 * q^82 + 13428 * q^83 - 115824 * q^84 + 35464 * q^85 - 170400 * q^86 - 16 * q^87 - 142256 * q^88 - 84116 * q^89 - 111624 * q^90 - 26920 * q^91 - 159616 * q^92 - 80128 * q^93 - 35920 * q^94 - 50696 * q^95 + 51904 * q^96 + 10292 * q^97 + 152576 * q^98 + 44636 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(320))\)

We only show spaces with odd 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
320.5.b	\(\chi_{320}(191, \cdot)\)	320.5.b.a	4	1
		320.5.b.b	4
		320.5.b.c	8
		320.5.b.d	8
		320.5.b.e	8
320.5.e	\(\chi_{320}(159, \cdot)\)	320.5.e.a	16	1
		320.5.e.b	32
320.5.g	\(\chi_{320}(31, \cdot)\)	320.5.g.a	8	1
		320.5.g.b	24
320.5.h	\(\chi_{320}(319, \cdot)\)	320.5.h.a	1	1
		320.5.h.b	1
		320.5.h.c	2
		320.5.h.d	2
		320.5.h.e	8
		320.5.h.f	8
		320.5.h.g	12
		320.5.h.h	12
320.5.i	\(\chi_{320}(177, \cdot)\)	320.5.i.a	92	2
320.5.k	\(\chi_{320}(79, \cdot)\)	320.5.k.a	92	2
320.5.m	\(\chi_{320}(33, \cdot)\)	320.5.m.a	16	2
		320.5.m.b	16
		320.5.m.c	32
		320.5.m.d	32
320.5.p	\(\chi_{320}(193, \cdot)\)	320.5.p.a	2	2
		320.5.p.b	2
		320.5.p.c	2
		320.5.p.d	2
		320.5.p.e	2
		320.5.p.f	2
		320.5.p.g	2
		320.5.p.h	2
		320.5.p.i	2
		320.5.p.j	2
		320.5.p.k	4
		320.5.p.l	4
		320.5.p.m	4
		320.5.p.n	4
		320.5.p.o	6
		320.5.p.p	6
		320.5.p.q	8
		320.5.p.r	12
		320.5.p.s	12
		320.5.p.t	12
320.5.r	\(\chi_{320}(111, \cdot)\)	320.5.r.a	64	2
320.5.t	\(\chi_{320}(17, \cdot)\)	320.5.t.a	92	2
320.5.v	\(\chi_{320}(57, \cdot)\)	None	0	4
320.5.w	\(\chi_{320}(71, \cdot)\)	None	0	4
320.5.y	\(\chi_{320}(39, \cdot)\)	None	0	4
320.5.bb	\(\chi_{320}(137, \cdot)\)	None	0	4
320.5.bc	\(\chi_{320}(53, \cdot)\)	n/a	1520	8
320.5.bg	\(\chi_{320}(11, \cdot)\)	n/a	1024	8
320.5.bh	\(\chi_{320}(19, \cdot)\)	n/a	1520	8
320.5.bi	\(\chi_{320}(13, \cdot)\)	n/a	1520	8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

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