Space of modular forms of level 320 and weight 6

• Label: 320.6
• Level: 320
• Weight: 6
• Dimension: 7854
• Nonzero newspaces: 14
• Sturm bound: 36864
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(36864\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(320))\).

	Total	New	Old
Modular forms	15648	7986	7662
Cusp forms	15072	7854	7218
Eisenstein series	576	132	444

Trace form

7854 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 24 * q^5 - 48 * q^6 - 8 * q^7 - 16 * q^8 + 466 * q^9 - 24 * q^10 - 1244 * q^11 - 16 * q^12 + 448 * q^13 - 16 * q^14 + 1780 * q^15 - 48 * q^16 + 1588 * q^17 - 16 * q^18 - 4732 * q^19 - 24 * q^20 - 10488 * q^21 - 27200 * q^22 - 8 * q^23 + 44064 * q^24 + 12434 * q^25 + 51872 * q^26 + 8424 * q^27 - 8736 * q^28 - 16304 * q^29 - 64904 * q^30 - 23120 * q^31 - 74336 * q^32 - 44416 * q^33 - 25536 * q^34 + 8620 * q^35 + 124592 * q^36 + 46880 * q^37 + 139264 * q^38 - 16 * q^39 + 62336 * q^40 - 26684 * q^41 - 92736 * q^42 - 30772 * q^43 - 131040 * q^44 + 23500 * q^45 - 48 * q^46 + 88344 * q^47 - 16 * q^48 + 24886 * q^49 + 137040 * q^50 - 89048 * q^51 - 146992 * q^52 - 77728 * q^53 - 466576 * q^54 + 220080 * q^55 - 301888 * q^56 - 72672 * q^57 - 52000 * q^58 - 175316 * q^59 + 197832 * q^60 + 100256 * q^61 + 350736 * q^62 - 793800 * q^63 + 749744 * q^64 - 155296 * q^65 + 509200 * q^66 - 216556 * q^67 + 14288 * q^68 + 283112 * q^69 - 286968 * q^70 + 863008 * q^71 - 828160 * q^72 + 250540 * q^73 - 755456 * q^74 + 291984 * q^75 - 537008 * q^76 - 375480 * q^77 - 665344 * q^78 - 1315728 * q^79 + 299840 * q^80 - 306266 * q^81 + 1006224 * q^82 + 202788 * q^83 + 1970064 * q^84 + 312224 * q^85 + 1443680 * q^86 + 564360 * q^87 + 446544 * q^88 + 331468 * q^89 - 284424 * q^90 + 196520 * q^91 - 1842560 * q^92 + 8768 * q^93 - 1642576 * q^94 - 327252 * q^95 - 2428736 * q^96 - 1673788 * q^97 - 1914624 * q^98 - 1069828 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.6.a	\(\chi_{320}(1, \cdot)\)	320.6.a.a	1	1
		320.6.a.b	1
		320.6.a.c	1
		320.6.a.d	1
		320.6.a.e	1
		320.6.a.f	1
		320.6.a.g	1
		320.6.a.h	1
		320.6.a.i	1
		320.6.a.j	1
		320.6.a.k	1
		320.6.a.l	1
		320.6.a.m	1
		320.6.a.n	1
		320.6.a.o	1
		320.6.a.p	1
		320.6.a.q	2
		320.6.a.r	2
		320.6.a.s	2
		320.6.a.t	2
		320.6.a.u	2
		320.6.a.v	2
		320.6.a.w	2
		320.6.a.x	3
		320.6.a.y	3
		320.6.a.z	4
320.6.c	\(\chi_{320}(129, \cdot)\)	320.6.c.a	2	1
		320.6.c.b	2
		320.6.c.c	2
		320.6.c.d	2
		320.6.c.e	2
		320.6.c.f	2
		320.6.c.g	2
		320.6.c.h	4
		320.6.c.i	8
		320.6.c.j	8
		320.6.c.k	12
		320.6.c.l	12
320.6.d	\(\chi_{320}(161, \cdot)\)	320.6.d.a	8	1
		320.6.d.b	8
		320.6.d.c	12
		320.6.d.d	12
320.6.f	\(\chi_{320}(289, \cdot)\)	320.6.f.a	4	1
		320.6.f.b	8
		320.6.f.c	16
		320.6.f.d	32
320.6.j	\(\chi_{320}(47, \cdot)\)	n/a	116	2
320.6.l	\(\chi_{320}(81, \cdot)\)	320.6.l.a	80	2
320.6.n	\(\chi_{320}(63, \cdot)\)	n/a	116	2
320.6.o	\(\chi_{320}(223, \cdot)\)	n/a	120	2
320.6.q	\(\chi_{320}(49, \cdot)\)	n/a	116	2
320.6.s	\(\chi_{320}(207, \cdot)\)	n/a	116	2
320.6.u	\(\chi_{320}(87, \cdot)\)	None	0	4
320.6.x	\(\chi_{320}(41, \cdot)\)	None	0	4
320.6.z	\(\chi_{320}(9, \cdot)\)	None	0	4
320.6.ba	\(\chi_{320}(7, \cdot)\)	None	0	4
320.6.bd	\(\chi_{320}(43, \cdot)\)	n/a	1904	8
320.6.be	\(\chi_{320}(21, \cdot)\)	n/a	1280	8
320.6.bf	\(\chi_{320}(29, \cdot)\)	n/a	1904	8
320.6.bj	\(\chi_{320}(3, \cdot)\)	n/a	1904	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

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