Space of modular forms of level 160 and weight 5

• Label: 160.5
• Level: 160
• Weight: 5
• Dimension: 1554
• Nonzero newspaces: 10
• Newform subspaces: 19
• Sturm bound: 7680
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(7680\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(160))\).

	Total	New	Old
Modular forms	3200	1614	1586
Cusp forms	2944	1554	1390
Eisenstein series	256	60	196

Trace form

1554 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 + 12 * q^5 - 24 * q^6 - 4 * q^7 - 8 * q^8 - 74 * q^9 + 188 * q^10 - 212 * q^11 - 1448 * q^12 - 472 * q^13 - 872 * q^14 - 4 * q^15 + 1216 * q^16 + 860 * q^17 + 3232 * q^18 + 1404 * q^19 + 1188 * q^20 + 1768 * q^21 - 3792 * q^22 + 2300 * q^23 - 5040 * q^24 - 1090 * q^25 + 5376 * q^26 - 10952 * q^27 + 5632 * q^28 - 440 * q^29 + 2412 * q^30 + 232 * q^31 - 2528 * q^32 + 2128 * q^33 - 7216 * q^34 + 3832 * q^35 - 5888 * q^36 + 1352 * q^37 - 5048 * q^38 + 5368 * q^39 - 6776 * q^40 - 7812 * q^41 - 7328 * q^42 - 16712 * q^43 - 12440 * q^44 + 5104 * q^45 - 5848 * q^46 + 5764 * q^47 + 9872 * q^48 + 12330 * q^49 + 3420 * q^50 - 3360 * q^51 + 16296 * q^52 + 16456 * q^53 + 51888 * q^54 + 9268 * q^55 + 46992 * q^56 - 12080 * q^57 + 29232 * q^58 + 5564 * q^59 - 4936 * q^60 - 35560 * q^61 - 30592 * q^62 - 9940 * q^63 - 47120 * q^64 - 17840 * q^65 - 66104 * q^66 - 18888 * q^67 - 19456 * q^68 + 78968 * q^69 + 26760 * q^70 - 19984 * q^71 + 38968 * q^72 + 3092 * q^73 + 37480 * q^74 + 13684 * q^75 + 41576 * q^76 - 18440 * q^77 + 18968 * q^78 + 100336 * q^79 - 23976 * q^80 - 12534 * q^81 - 42408 * q^82 - 31688 * q^83 - 50784 * q^84 - 56992 * q^85 + 30048 * q^86 - 147520 * q^87 - 4128 * q^88 - 40812 * q^89 - 55848 * q^90 - 86032 * q^91 + 92656 * q^92 + 44528 * q^93 + 131568 * q^94 + 27832 * q^95 + 119136 * q^96 + 43084 * q^97 - 20848 * q^98 + 140420 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.5.b	\(\chi_{160}(31, \cdot)\)	160.5.b.a	8	1
		160.5.b.b	8
160.5.e	\(\chi_{160}(79, \cdot)\)	160.5.e.a	1	1
		160.5.e.b	1
		160.5.e.c	20
160.5.g	\(\chi_{160}(111, \cdot)\)	160.5.g.a	16	1
160.5.h	\(\chi_{160}(159, \cdot)\)	160.5.h.a	12	1
		160.5.h.b	12
160.5.i	\(\chi_{160}(57, \cdot)\)	None	0	2
160.5.k	\(\chi_{160}(39, \cdot)\)	None	0	2
160.5.m	\(\chi_{160}(17, \cdot)\)	160.5.m.a	44	2
160.5.p	\(\chi_{160}(33, \cdot)\)	160.5.p.a	2	2
		160.5.p.b	2
		160.5.p.c	8
		160.5.p.d	12
		160.5.p.e	12
		160.5.p.f	12
160.5.r	\(\chi_{160}(71, \cdot)\)	None	0	2
160.5.t	\(\chi_{160}(137, \cdot)\)	None	0	2
160.5.v	\(\chi_{160}(13, \cdot)\)	160.5.v.a	376	4
160.5.w	\(\chi_{160}(11, \cdot)\)	160.5.w.a	256	4
160.5.y	\(\chi_{160}(19, \cdot)\)	160.5.y.a	376	4
160.5.bb	\(\chi_{160}(53, \cdot)\)	160.5.bb.a	376	4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

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