Space of modular forms of level 320 and weight 4

• Label: 320.4
• Level: 320
• Weight: 4
• Dimension: 4686
• Nonzero newspaces: 14
• Sturm bound: 24576
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(24576\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(320))\).

	Total	New	Old
Modular forms	9504	4818	4686
Cusp forms	8928	4686	4242
Eisenstein series	576	132	444

Trace form

4686 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 24 * q^5 - 48 * q^6 - 8 * q^7 - 16 * q^8 + 34 * q^9 - 24 * q^10 + 4 * q^11 - 16 * q^12 - 160 * q^13 - 16 * q^14 - 140 * q^15 - 48 * q^16 - 236 * q^17 - 16 * q^18 - 60 * q^19 - 24 * q^20 - 24 * q^21 - 960 * q^22 - 8 * q^23 - 2016 * q^24 - 206 * q^25 + 32 * q^26 + 360 * q^27 + 1504 * q^28 + 784 * q^29 + 2296 * q^30 + 688 * q^31 + 2464 * q^32 + 1952 * q^33 + 1984 * q^34 + 460 * q^35 + 1712 * q^36 + 1024 * q^37 - 896 * q^38 - 16 * q^39 - 1664 * q^40 - 2108 * q^41 - 6336 * q^42 - 1684 * q^43 - 2016 * q^44 - 1508 * q^45 - 48 * q^46 - 1896 * q^47 - 16 * q^48 - 2154 * q^49 + 2832 * q^50 - 8984 * q^51 + 6608 * q^52 - 832 * q^53 + 3440 * q^54 - 592 * q^55 - 832 * q^56 + 1920 * q^57 - 4768 * q^58 + 8908 * q^59 - 4920 * q^60 + 2112 * q^61 - 6000 * q^62 + 12600 * q^63 - 12112 * q^64 - 1984 * q^65 - 11120 * q^66 + 8340 * q^67 - 4144 * q^68 - 1720 * q^69 - 2040 * q^70 + 1312 * q^71 + 1280 * q^72 + 300 * q^73 + 5248 * q^74 - 528 * q^75 + 11856 * q^76 + 744 * q^77 + 3968 * q^78 - 13840 * q^79 - 4288 * q^80 - 3866 * q^81 - 13936 * q^82 + 228 * q^83 - 8304 * q^84 + 3024 * q^85 + 992 * q^86 + 2568 * q^87 + 6224 * q^88 + 6412 * q^89 + 9336 * q^90 + 3240 * q^91 + 25216 * q^92 + 6848 * q^93 + 17840 * q^94 - 852 * q^95 + 25792 * q^96 + 11428 * q^97 + 24192 * q^98 + 3644 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.4.a	\(\chi_{320}(1, \cdot)\)	320.4.a.a	1	1
		320.4.a.b	1
		320.4.a.c	1
		320.4.a.d	1
		320.4.a.e	1
		320.4.a.f	1
		320.4.a.g	1
		320.4.a.h	1
		320.4.a.i	1
		320.4.a.j	1
		320.4.a.k	1
		320.4.a.l	1
		320.4.a.m	1
		320.4.a.n	1
		320.4.a.o	2
		320.4.a.p	2
		320.4.a.q	2
		320.4.a.r	2
		320.4.a.s	2
320.4.c	\(\chi_{320}(129, \cdot)\)	320.4.c.a	2	1
		320.4.c.b	2
		320.4.c.c	2
		320.4.c.d	2
		320.4.c.e	2
		320.4.c.f	4
		320.4.c.g	4
		320.4.c.h	4
		320.4.c.i	4
		320.4.c.j	8
320.4.d	\(\chi_{320}(161, \cdot)\)	320.4.d.a	4	1
		320.4.d.b	4
		320.4.d.c	8
		320.4.d.d	8
320.4.f	\(\chi_{320}(289, \cdot)\)	320.4.f.a	4	1
		320.4.f.b	8
		320.4.f.c	24
320.4.j	\(\chi_{320}(47, \cdot)\)	320.4.j.a	68	2
320.4.l	\(\chi_{320}(81, \cdot)\)	320.4.l.a	48	2
320.4.n	\(\chi_{320}(63, \cdot)\)	320.4.n.a	2	2
		320.4.n.b	2
		320.4.n.c	2
		320.4.n.d	2
		320.4.n.e	4
		320.4.n.f	8
		320.4.n.g	8
		320.4.n.h	8
		320.4.n.i	8
		320.4.n.j	12
		320.4.n.k	12
320.4.o	\(\chi_{320}(223, \cdot)\)	320.4.o.a	12	2
		320.4.o.b	12
		320.4.o.c	24
		320.4.o.d	24
320.4.q	\(\chi_{320}(49, \cdot)\)	320.4.q.a	68	2
320.4.s	\(\chi_{320}(207, \cdot)\)	320.4.s.a	68	2
320.4.u	\(\chi_{320}(87, \cdot)\)	None	0	4
320.4.x	\(\chi_{320}(41, \cdot)\)	None	0	4
320.4.z	\(\chi_{320}(9, \cdot)\)	None	0	4
320.4.ba	\(\chi_{320}(7, \cdot)\)	None	0	4
320.4.bd	\(\chi_{320}(43, \cdot)\)	n/a	1136	8
320.4.be	\(\chi_{320}(21, \cdot)\)	n/a	768	8
320.4.bf	\(\chi_{320}(29, \cdot)\)	n/a	1136	8
320.4.bj	\(\chi_{320}(3, \cdot)\)	n/a	1136	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

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