Space of modular forms of level 160 and weight 4

• Label: 160.4
• Level: 160
• Weight: 4
• Dimension: 1158
• Nonzero newspaces: 10
• Newform subspaces: 24
• Sturm bound: 6144
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 24 \)
Sturm bound:			\(6144\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(160))\).

	Total	New	Old
Modular forms	2432	1218	1214
Cusp forms	2176	1158	1018
Eisenstein series	256	60	196

Trace form

1158 * q - 8 * q^2 - 4 * q^3 - 8 * q^4 - 14 * q^5 - 24 * q^6 - 36 * q^7 - 8 * q^8 - 106 * q^9 - 132 * q^10 - 16 * q^11 + 88 * q^12 + 228 * q^13 + 408 * q^14 + 100 * q^15 + 576 * q^16 + 356 * q^17 + 352 * q^18 - 8 * q^19 - 92 * q^20 - 536 * q^21 - 400 * q^22 - 1268 * q^23 + 80 * q^24 - 230 * q^25 - 64 * q^26 + 416 * q^27 - 768 * q^28 - 180 * q^29 - 1204 * q^30 + 1848 * q^31 - 1248 * q^32 + 824 * q^33 - 1072 * q^34 + 904 * q^35 - 2944 * q^36 - 356 * q^37 - 1976 * q^38 - 1072 * q^39 + 520 * q^40 + 244 * q^41 + 4512 * q^42 - 756 * q^43 + 4072 * q^44 + 1574 * q^45 + 2856 * q^46 + 924 * q^47 + 4880 * q^48 + 510 * q^49 + 3548 * q^50 + 1256 * q^51 + 5032 * q^52 - 2052 * q^53 + 2160 * q^54 - 556 * q^55 - 2416 * q^56 - 1864 * q^57 - 6416 * q^58 - 2760 * q^59 - 4744 * q^60 + 1844 * q^61 - 6784 * q^62 - 3740 * q^63 - 2192 * q^64 + 2436 * q^65 + 1160 * q^66 - 2236 * q^67 + 384 * q^68 + 3544 * q^69 + 168 * q^70 - 976 * q^71 - 2120 * q^72 - 884 * q^73 - 1688 * q^74 - 1104 * q^75 + 1640 * q^76 - 8264 * q^77 + 408 * q^78 - 5008 * q^79 - 2344 * q^80 - 6874 * q^81 + 1112 * q^82 - 7564 * q^83 - 4832 * q^84 - 3748 * q^85 - 2912 * q^86 + 4536 * q^87 - 3744 * q^88 + 4268 * q^89 + 24 * q^90 + 8880 * q^91 - 9232 * q^92 - 144 * q^93 - 11024 * q^94 + 8656 * q^95 - 10912 * q^96 + 2516 * q^97 - 9840 * q^98 + 10832 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.4.a	\(\chi_{160}(1, \cdot)\)	160.4.a.a	1	1
		160.4.a.b	1
		160.4.a.c	2
		160.4.a.d	2
		160.4.a.e	2
		160.4.a.f	2
		160.4.a.g	2
160.4.c	\(\chi_{160}(129, \cdot)\)	160.4.c.a	2	1
		160.4.c.b	4
		160.4.c.c	4
		160.4.c.d	8
160.4.d	\(\chi_{160}(81, \cdot)\)	160.4.d.a	12	1
160.4.f	\(\chi_{160}(49, \cdot)\)	160.4.f.a	16	1
160.4.j	\(\chi_{160}(87, \cdot)\)	None	0	2
160.4.l	\(\chi_{160}(41, \cdot)\)	None	0	2
160.4.n	\(\chi_{160}(63, \cdot)\)	160.4.n.a	2	2
		160.4.n.b	2
		160.4.n.c	8
		160.4.n.d	8
		160.4.n.e	8
		160.4.n.f	8
160.4.o	\(\chi_{160}(47, \cdot)\)	160.4.o.a	32	2
160.4.q	\(\chi_{160}(9, \cdot)\)	None	0	2
160.4.s	\(\chi_{160}(7, \cdot)\)	None	0	2
160.4.u	\(\chi_{160}(43, \cdot)\)	160.4.u.a	280	4
160.4.x	\(\chi_{160}(21, \cdot)\)	160.4.x.a	192	4
160.4.z	\(\chi_{160}(29, \cdot)\)	160.4.z.a	280	4
160.4.ba	\(\chi_{160}(3, \cdot)\)	160.4.ba.a	280	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

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