Space of modular forms of level 160 and weight 2

• Label: 160.2
• Level: 160
• Weight: 2
• Dimension: 366
• Nonzero newspaces: 10
• Newform subspaces: 18
• Sturm bound: 3072
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(3072\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(160))\).

	Total	New	Old
Modular forms	896	426	470
Cusp forms	641	366	275
Eisenstein series	255	60	195

Trace form

366 * q - 8 * q^2 - 4 * q^3 - 8 * q^4 - 10 * q^5 - 24 * q^6 - 4 * q^7 - 8 * q^8 - 10 * q^9 - 20 * q^10 - 16 * q^11 - 40 * q^12 - 20 * q^13 - 40 * q^14 - 12 * q^15 - 64 * q^16 - 12 * q^17 - 48 * q^18 - 8 * q^19 - 28 * q^20 - 24 * q^21 - 32 * q^22 - 20 * q^23 + 16 * q^24 - 14 * q^25 + 16 * q^26 - 64 * q^27 + 32 * q^28 + 4 * q^29 + 20 * q^30 - 72 * q^31 + 32 * q^32 - 56 * q^33 + 16 * q^34 - 56 * q^35 + 32 * q^36 - 44 * q^37 - 24 * q^38 - 80 * q^39 - 24 * q^40 - 92 * q^41 - 48 * q^42 - 52 * q^43 - 88 * q^44 - 70 * q^45 - 88 * q^46 - 36 * q^47 - 112 * q^48 - 26 * q^49 - 52 * q^50 - 24 * q^51 - 24 * q^52 - 76 * q^53 - 32 * q^54 + 4 * q^55 - 48 * q^56 + 8 * q^57 + 56 * q^59 + 56 * q^60 - 68 * q^61 + 32 * q^62 + 100 * q^63 + 112 * q^64 + 12 * q^65 + 152 * q^66 + 100 * q^67 + 64 * q^68 + 24 * q^69 + 144 * q^70 + 80 * q^71 + 184 * q^72 + 60 * q^73 + 136 * q^74 + 80 * q^75 + 104 * q^76 + 56 * q^77 + 216 * q^78 + 48 * q^79 + 152 * q^80 + 94 * q^81 + 152 * q^82 - 44 * q^83 + 256 * q^84 + 68 * q^85 + 144 * q^86 - 72 * q^87 + 160 * q^88 + 28 * q^89 + 216 * q^90 - 80 * q^91 + 208 * q^92 + 112 * q^93 + 80 * q^94 - 64 * q^95 + 96 * q^96 - 28 * q^97 + 80 * q^98 - 112 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.2.a	\(\chi_{160}(1, \cdot)\)	160.2.a.a	1	1
		160.2.a.b	1
		160.2.a.c	2
160.2.c	\(\chi_{160}(129, \cdot)\)	160.2.c.a	2	1
		160.2.c.b	4
160.2.d	\(\chi_{160}(81, \cdot)\)	160.2.d.a	4	1
160.2.f	\(\chi_{160}(49, \cdot)\)	160.2.f.a	4	1
160.2.j	\(\chi_{160}(87, \cdot)\)	None	0	2
160.2.l	\(\chi_{160}(41, \cdot)\)	None	0	2
160.2.n	\(\chi_{160}(63, \cdot)\)	160.2.n.a	2	2
		160.2.n.b	2
		160.2.n.c	2
		160.2.n.d	2
		160.2.n.e	2
		160.2.n.f	2
160.2.o	\(\chi_{160}(47, \cdot)\)	160.2.o.a	8	2
160.2.q	\(\chi_{160}(9, \cdot)\)	None	0	2
160.2.s	\(\chi_{160}(7, \cdot)\)	None	0	2
160.2.u	\(\chi_{160}(43, \cdot)\)	160.2.u.a	88	4
160.2.x	\(\chi_{160}(21, \cdot)\)	160.2.x.a	64	4
160.2.z	\(\chi_{160}(29, \cdot)\)	160.2.z.a	88	4
160.2.ba	\(\chi_{160}(3, \cdot)\)	160.2.ba.a	88	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

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