Space of modular forms of level 160 and weight 3

• Label: 160.3
• Level: 160
• Weight: 3
• Dimension: 762
• Nonzero newspaces: 10
• Newform subspaces: 19
• Sturm bound: 4608
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(4608\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(160))\).

	Total	New	Old
Modular forms	1664	822	842
Cusp forms	1408	762	646
Eisenstein series	256	60	196

Trace form

762 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 16 * q^5 - 24 * q^6 - 4 * q^7 - 8 * q^8 + 22 * q^9 + 28 * q^10 + 12 * q^11 + 88 * q^12 + 48 * q^13 + 24 * q^14 - 4 * q^15 - 64 * q^16 - 84 * q^17 - 128 * q^18 - 68 * q^19 - 92 * q^20 - 152 * q^21 - 304 * q^22 + 124 * q^23 - 432 * q^24 + 22 * q^25 - 224 * q^26 + 280 * q^27 - 128 * q^28 + 128 * q^29 - 36 * q^30 + 104 * q^31 + 32 * q^32 + 160 * q^33 + 80 * q^34 - 8 * q^35 + 640 * q^36 + 192 * q^37 + 776 * q^38 - 392 * q^39 + 392 * q^40 + 44 * q^41 + 832 * q^42 - 296 * q^43 + 360 * q^44 - 188 * q^45 + 40 * q^46 - 188 * q^47 - 112 * q^48 - 366 * q^49 - 324 * q^50 - 672 * q^51 - 856 * q^52 - 64 * q^53 - 1200 * q^54 - 364 * q^55 - 1136 * q^56 - 416 * q^57 - 1072 * q^58 - 420 * q^59 - 712 * q^60 - 224 * q^61 - 448 * q^62 - 244 * q^63 - 272 * q^64 - 424 * q^65 - 536 * q^66 + 152 * q^67 - 512 * q^68 - 712 * q^69 - 648 * q^70 + 240 * q^71 - 200 * q^72 - 380 * q^73 + 168 * q^74 + 52 * q^75 + 616 * q^76 - 520 * q^77 + 152 * q^78 + 1008 * q^79 - 168 * q^80 + 642 * q^81 - 808 * q^82 + 1432 * q^83 - 480 * q^84 + 392 * q^85 - 512 * q^86 + 1376 * q^87 + 224 * q^88 + 452 * q^89 + 1752 * q^90 + 752 * q^91 + 624 * q^92 + 752 * q^93 + 1584 * q^94 + 472 * q^95 + 2400 * q^96 + 796 * q^97 + 1552 * q^98 + 68 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.3.b	\(\chi_{160}(31, \cdot)\)	160.3.b.a	4	1
		160.3.b.b	4
160.3.e	\(\chi_{160}(79, \cdot)\)	160.3.e.a	1	1
		160.3.e.b	1
		160.3.e.c	8
160.3.g	\(\chi_{160}(111, \cdot)\)	160.3.g.a	8	1
160.3.h	\(\chi_{160}(159, \cdot)\)	160.3.h.a	6	1
		160.3.h.b	6
160.3.i	\(\chi_{160}(57, \cdot)\)	None	0	2
160.3.k	\(\chi_{160}(39, \cdot)\)	None	0	2
160.3.m	\(\chi_{160}(17, \cdot)\)	160.3.m.a	20	2
160.3.p	\(\chi_{160}(33, \cdot)\)	160.3.p.a	2	2
		160.3.p.b	2
		160.3.p.c	4
		160.3.p.d	4
		160.3.p.e	6
		160.3.p.f	6
160.3.r	\(\chi_{160}(71, \cdot)\)	None	0	2
160.3.t	\(\chi_{160}(137, \cdot)\)	None	0	2
160.3.v	\(\chi_{160}(13, \cdot)\)	160.3.v.a	184	4
160.3.w	\(\chi_{160}(11, \cdot)\)	160.3.w.a	128	4
160.3.y	\(\chi_{160}(19, \cdot)\)	160.3.y.a	184	4
160.3.bb	\(\chi_{160}(53, \cdot)\)	160.3.bb.a	184	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

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