Space of modular forms of level 320 and weight 10

• Label: 320.10
• Level: 320
• Weight: 10
• Dimension: 14190
• Nonzero newspaces: 14
• Sturm bound: 61440
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(61440\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(320))\).

	Total	New	Old
Modular forms	27936	14322	13614
Cusp forms	27360	14190	13170
Eisenstein series	576	132	444

Trace form

14190 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 24 * q^5 - 48 * q^6 - 8 * q^7 - 16 * q^8 + 39346 * q^9 - 24 * q^10 + 131684 * q^11 - 16 * q^12 - 389248 * q^13 - 16 * q^14 + 404980 * q^15 - 48 * q^16 - 816012 * q^17 - 16 * q^18 - 961788 * q^19 - 24 * q^20 + 3918408 * q^21 - 7152704 * q^22 - 8 * q^23 - 24194016 * q^24 - 6887086 * q^25 + 4211872 * q^26 + 12728808 * q^27 + 43582944 * q^28 + 2533584 * q^29 - 44263304 * q^30 - 22164560 * q^31 - 58882656 * q^32 + 381248 * q^33 + 77073984 * q^34 + 23026540 * q^35 + 221001392 * q^36 - 34002336 * q^37 - 133894656 * q^38 - 16 * q^39 - 97089664 * q^40 - 2322492 * q^41 + 449118144 * q^42 - 69762164 * q^43 - 292354016 * q^44 + 14308780 * q^45 - 48 * q^46 + 195187224 * q^47 - 16 * q^48 - 29078922 * q^49 - 182758320 * q^50 + 665350312 * q^51 + 50454992 * q^52 - 322945888 * q^53 + 1292464496 * q^54 - 280217680 * q^55 - 406326080 * q^56 + 755186784 * q^57 - 1710306592 * q^58 + 1341307628 * q^59 - 230939448 * q^60 - 418731168 * q^61 + 1195218960 * q^62 - 3150592200 * q^63 + 2729619632 * q^64 + 741098784 * q^65 - 372027632 * q^66 + 2208949524 * q^67 - 2008655920 * q^68 - 1214947288 * q^69 - 1869092088 * q^70 + 1428608800 * q^71 + 1429458176 * q^72 + 79439276 * q^73 + 4364366592 * q^74 - 1513502256 * q^75 + 1777421904 * q^76 - 1200290040 * q^77 - 10487574784 * q^78 + 5249382768 * q^79 + 5193915200 * q^80 - 1542943706 * q^81 - 6272811376 * q^82 - 1683060572 * q^83 - 12297543792 * q^84 + 3066377664 * q^85 + 1977656672 * q^86 + 4701903240 * q^87 + 9881370704 * q^88 + 7515983436 * q^89 + 7222409976 * q^90 - 1533093976 * q^91 - 3458979200 * q^92 - 7535004352 * q^93 - 13420980304 * q^94 - 125426772 * q^95 - 20733163328 * q^96 - 2196521980 * q^97 - 5087722752 * q^98 + 4327823996 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.10.a	\(\chi_{320}(1, \cdot)\)	320.10.a.a	1	1
		320.10.a.b	1
		320.10.a.c	1
		320.10.a.d	1
		320.10.a.e	1
		320.10.a.f	1
		320.10.a.g	1
		320.10.a.h	1
		320.10.a.i	1
		320.10.a.j	1
		320.10.a.k	2
		320.10.a.l	2
		320.10.a.m	2
		320.10.a.n	2
		320.10.a.o	2
		320.10.a.p	2
		320.10.a.q	2
		320.10.a.r	2
		320.10.a.s	2
		320.10.a.t	2
		320.10.a.u	3
		320.10.a.v	3
		320.10.a.w	4
		320.10.a.x	4
		320.10.a.y	4
		320.10.a.z	4
		320.10.a.ba	4
		320.10.a.bb	5
		320.10.a.bc	5
		320.10.a.bd	6
320.10.c	\(\chi_{320}(129, \cdot)\)	n/a	106	1
320.10.d	\(\chi_{320}(161, \cdot)\)	320.10.d.a	12	1
		320.10.d.b	12
		320.10.d.c	24
		320.10.d.d	24
320.10.f	\(\chi_{320}(289, \cdot)\)	n/a	108	1
320.10.j	\(\chi_{320}(47, \cdot)\)	n/a	212	2
320.10.l	\(\chi_{320}(81, \cdot)\)	n/a	144	2
320.10.n	\(\chi_{320}(63, \cdot)\)	n/a	212	2
320.10.o	\(\chi_{320}(223, \cdot)\)	n/a	216	2
320.10.q	\(\chi_{320}(49, \cdot)\)	n/a	212	2
320.10.s	\(\chi_{320}(207, \cdot)\)	n/a	212	2
320.10.u	\(\chi_{320}(87, \cdot)\)	None	0	4
320.10.x	\(\chi_{320}(41, \cdot)\)	None	0	4
320.10.z	\(\chi_{320}(9, \cdot)\)	None	0	4
320.10.ba	\(\chi_{320}(7, \cdot)\)	None	0	4
320.10.bd	\(\chi_{320}(43, \cdot)\)	n/a	3440	8
320.10.be	\(\chi_{320}(21, \cdot)\)	n/a	2304	8
320.10.bf	\(\chi_{320}(29, \cdot)\)	n/a	3440	8
320.10.bj	\(\chi_{320}(3, \cdot)\)	n/a	3440	8

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

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