Space of modular forms of level 320 and weight 2

• Label: 320.2
• Level: 320
• Weight: 2
• Dimension: 1518
• Nonzero newspaces: 14
• Newform subspaces: 42
• Sturm bound: 12288
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 14 \)
Newform subspaces:			\( 42 \)
Sturm bound:			\(12288\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(320))\).

	Total	New	Old
Modular forms	3360	1650	1710
Cusp forms	2785	1518	1267
Eisenstein series	575	132	443

Trace form

1518 * q - 16 * q^2 - 12 * q^3 - 16 * q^4 - 24 * q^5 - 48 * q^6 - 8 * q^7 - 16 * q^8 - 14 * q^9 - 24 * q^10 - 28 * q^11 - 16 * q^12 - 16 * q^14 - 12 * q^15 - 48 * q^16 - 12 * q^17 - 16 * q^18 + 4 * q^19 - 24 * q^20 - 56 * q^21 - 32 * q^22 - 8 * q^23 - 96 * q^24 - 46 * q^25 - 128 * q^26 - 24 * q^27 - 96 * q^28 - 48 * q^29 - 104 * q^30 - 80 * q^31 - 96 * q^32 - 64 * q^33 - 96 * q^34 - 20 * q^35 - 208 * q^36 - 32 * q^37 - 96 * q^38 - 16 * q^39 - 64 * q^40 - 60 * q^41 - 96 * q^42 + 12 * q^43 - 32 * q^44 - 20 * q^45 - 48 * q^46 + 24 * q^47 - 16 * q^48 - 10 * q^49 - 88 * q^51 + 80 * q^52 + 32 * q^53 + 112 * q^54 - 80 * q^55 + 64 * q^56 - 32 * q^57 + 128 * q^58 - 148 * q^59 + 72 * q^60 - 32 * q^61 + 48 * q^62 - 200 * q^63 + 176 * q^64 - 96 * q^65 + 112 * q^66 - 236 * q^67 + 80 * q^68 - 88 * q^69 + 72 * q^70 - 224 * q^71 + 128 * q^72 - 84 * q^73 + 96 * q^74 - 176 * q^75 + 80 * q^76 - 120 * q^77 + 32 * q^78 - 144 * q^79 - 64 * q^80 - 218 * q^81 - 176 * q^82 - 92 * q^83 - 240 * q^84 - 128 * q^85 - 256 * q^86 - 120 * q^87 - 176 * q^88 - 180 * q^89 - 168 * q^90 - 88 * q^91 - 320 * q^92 - 192 * q^93 - 208 * q^94 - 84 * q^95 - 320 * q^96 - 124 * q^97 - 288 * q^98 - 132 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.2.a	\(\chi_{320}(1, \cdot)\)	320.2.a.a	1	1
		320.2.a.b	1
		320.2.a.c	1
		320.2.a.d	1
		320.2.a.e	1
		320.2.a.f	1
		320.2.a.g	2
320.2.c	\(\chi_{320}(129, \cdot)\)	320.2.c.a	2	1
		320.2.c.b	2
		320.2.c.c	2
		320.2.c.d	4
320.2.d	\(\chi_{320}(161, \cdot)\)	320.2.d.a	4	1
		320.2.d.b	4
320.2.f	\(\chi_{320}(289, \cdot)\)	320.2.f.a	4	1
		320.2.f.b	8
320.2.j	\(\chi_{320}(47, \cdot)\)	320.2.j.a	2	2
		320.2.j.b	18
320.2.l	\(\chi_{320}(81, \cdot)\)	320.2.l.a	16	2
320.2.n	\(\chi_{320}(63, \cdot)\)	320.2.n.a	2	2
		320.2.n.b	2
		320.2.n.c	2
		320.2.n.d	2
		320.2.n.e	2
		320.2.n.f	2
		320.2.n.g	2
		320.2.n.h	2
		320.2.n.i	4
320.2.o	\(\chi_{320}(223, \cdot)\)	320.2.o.a	2	2
		320.2.o.b	2
		320.2.o.c	2
		320.2.o.d	2
		320.2.o.e	8
		320.2.o.f	8
320.2.q	\(\chi_{320}(49, \cdot)\)	320.2.q.a	2	2
		320.2.q.b	2
		320.2.q.c	16
320.2.s	\(\chi_{320}(207, \cdot)\)	320.2.s.a	2	2
		320.2.s.b	18
320.2.u	\(\chi_{320}(87, \cdot)\)	None	0	4
320.2.x	\(\chi_{320}(41, \cdot)\)	None	0	4
320.2.z	\(\chi_{320}(9, \cdot)\)	None	0	4
320.2.ba	\(\chi_{320}(7, \cdot)\)	None	0	4
320.2.bd	\(\chi_{320}(43, \cdot)\)	320.2.bd.a	368	8
320.2.be	\(\chi_{320}(21, \cdot)\)	320.2.be.a	256	8
320.2.bf	\(\chi_{320}(29, \cdot)\)	320.2.bf.a	368	8
320.2.bj	\(\chi_{320}(3, \cdot)\)	320.2.bj.a	368	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

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