Space of modular forms of level 80 and weight 5

• Label: 80.5
• Level: 80
• Weight: 5
• Dimension: 382
• Nonzero newspaces: 7
• Newform subspaces: 16
• Sturm bound: 1920
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1920\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	824	410	414
Cusp forms	712	382	330
Eisenstein series	112	28	84

Trace form

382 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 - 44 * q^5 - 144 * q^6 + 2 * q^7 + 176 * q^8 + 444 * q^9 + 92 * q^10 - 200 * q^11 + 656 * q^12 - 478 * q^13 - 96 * q^14 - 678 * q^15 + 320 * q^16 + 14 * q^17 - 2788 * q^18 + 1404 * q^19 - 1908 * q^20 - 12 * q^21 - 1808 * q^22 - 862 * q^23 + 3736 * q^24 + 2522 * q^25 + 6816 * q^26 + 2200 * q^27 + 5512 * q^28 - 1084 * q^29 - 2316 * q^30 - 140 * q^31 - 2224 * q^32 - 1324 * q^33 - 1264 * q^34 + 1246 * q^35 - 10856 * q^36 + 7122 * q^37 - 2944 * q^38 - 5384 * q^39 - 1184 * q^40 - 5644 * q^41 + 16120 * q^42 - 7874 * q^43 + 11624 * q^44 - 9134 * q^45 - 8648 * q^46 + 4314 * q^47 - 22424 * q^48 - 6952 * q^49 - 7088 * q^50 + 2748 * q^51 - 13872 * q^52 - 1422 * q^53 - 11208 * q^54 + 4000 * q^55 + 13888 * q^56 + 15392 * q^57 + 40904 * q^58 + 5564 * q^59 + 31960 * q^60 + 8808 * q^61 + 22936 * q^62 - 8014 * q^63 + 3296 * q^64 + 9946 * q^65 - 29528 * q^66 - 9762 * q^67 - 45312 * q^68 - 42496 * q^69 - 53536 * q^70 + 9404 * q^71 - 44392 * q^72 + 12902 * q^73 - 6568 * q^74 + 38362 * q^75 + 20520 * q^76 + 35228 * q^77 - 7592 * q^78 + 11328 * q^80 + 18046 * q^81 + 5288 * q^82 - 8162 * q^83 + 69424 * q^84 - 17438 * q^85 + 64680 * q^86 - 33440 * q^87 + 60656 * q^88 - 42264 * q^89 + 83288 * q^90 - 25732 * q^91 + 41248 * q^92 - 24972 * q^93 - 31952 * q^94 + 45400 * q^95 - 117680 * q^96 + 3582 * q^97 - 69964 * q^98 - 45948 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.5.b	\(\chi_{80}(31, \cdot)\)	80.5.b.a	4	1
		80.5.b.b	4
80.5.e	\(\chi_{80}(39, \cdot)\)	None	0	1
80.5.g	\(\chi_{80}(71, \cdot)\)	None	0	1
80.5.h	\(\chi_{80}(79, \cdot)\)	80.5.h.a	2	1
		80.5.h.b	2
		80.5.h.c	8
80.5.i	\(\chi_{80}(13, \cdot)\)	80.5.i.a	92	2
80.5.k	\(\chi_{80}(19, \cdot)\)	80.5.k.a	92	2
80.5.m	\(\chi_{80}(57, \cdot)\)	None	0	2
80.5.p	\(\chi_{80}(17, \cdot)\)	80.5.p.a	2	2
		80.5.p.b	2
		80.5.p.c	2
		80.5.p.d	2
		80.5.p.e	4
		80.5.p.f	4
		80.5.p.g	6
80.5.r	\(\chi_{80}(11, \cdot)\)	80.5.r.a	64	2
80.5.t	\(\chi_{80}(53, \cdot)\)	80.5.t.a	92	2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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