Space of modular forms of level 80 and weight 7

• Label: 80.7
• Level: 80
• Weight: 7
• Dimension: 580
• Nonzero newspaces: 7
• Newform subspaces: 15
• Sturm bound: 2688
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(2688\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	1208	608	600
Cusp forms	1096	580	516
Eisenstein series	112	28	84

Trace form

580 * q - 4 * q^2 - 2 * q^3 - 184 * q^4 + 58 * q^5 + 1008 * q^6 + 2 * q^7 - 1936 * q^8 - 1302 * q^9 + 1116 * q^10 - 2728 * q^11 + 4688 * q^12 + 5862 * q^13 - 15136 * q^14 - 1398 * q^15 + 15936 * q^16 - 18086 * q^17 + 3740 * q^18 - 7876 * q^19 + 16556 * q^20 + 38388 * q^21 - 50512 * q^22 + 8434 * q^23 + 65176 * q^24 + 14584 * q^25 - 117920 * q^26 - 12632 * q^27 - 123128 * q^28 + 62424 * q^29 + 123732 * q^30 + 61236 * q^31 + 303056 * q^32 - 66556 * q^33 - 116592 * q^34 + 31246 * q^35 - 236264 * q^36 - 133266 * q^37 + 140416 * q^38 - 508808 * q^39 + 206112 * q^40 + 183184 * q^41 + 219640 * q^42 + 731230 * q^43 - 192216 * q^44 + 30088 * q^45 - 615944 * q^46 - 83766 * q^47 - 275864 * q^48 - 705754 * q^49 - 342544 * q^50 - 906084 * q^51 + 2202512 * q^52 + 956382 * q^53 + 1468344 * q^54 + 821808 * q^55 - 732864 * q^56 + 804464 * q^57 - 2883832 * q^58 - 78308 * q^59 - 2372840 * q^60 - 2676364 * q^61 - 365672 * q^62 - 2345902 * q^63 + 2549984 * q^64 - 80498 * q^65 + 4300264 * q^66 + 3326734 * q^67 + 2299008 * q^68 + 3618560 * q^69 + 267296 * q^70 + 1317148 * q^71 - 270760 * q^72 - 721670 * q^73 - 2973480 * q^74 - 7676150 * q^75 - 5674776 * q^76 - 3723348 * q^77 - 3631592 * q^78 + 1388480 * q^80 + 3530860 * q^81 + 5857512 * q^82 + 7053550 * q^83 + 5026864 * q^84 + 1839846 * q^85 + 3016552 * q^86 - 907184 * q^87 - 7630864 * q^88 - 4866180 * q^89 - 4176328 * q^90 - 5001412 * q^91 - 6828384 * q^92 + 1910964 * q^93 - 1445840 * q^94 - 2473400 * q^95 + 11168848 * q^96 + 1550210 * q^97 + 9377524 * q^98 + 4794564 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.7.b	\(\chi_{80}(31, \cdot)\)	80.7.b.a	4	1
		80.7.b.b	8
80.7.e	\(\chi_{80}(39, \cdot)\)	None	0	1
80.7.g	\(\chi_{80}(71, \cdot)\)	None	0	1
80.7.h	\(\chi_{80}(79, \cdot)\)	80.7.h.a	2	1
		80.7.h.b	4
		80.7.h.c	12
80.7.i	\(\chi_{80}(13, \cdot)\)	80.7.i.a	140	2
80.7.k	\(\chi_{80}(19, \cdot)\)	80.7.k.a	140	2
80.7.m	\(\chi_{80}(57, \cdot)\)	None	0	2
80.7.p	\(\chi_{80}(17, \cdot)\)	80.7.p.a	2	2
		80.7.p.b	4
		80.7.p.c	4
		80.7.p.d	6
		80.7.p.e	8
		80.7.p.f	10
80.7.r	\(\chi_{80}(11, \cdot)\)	80.7.r.a	96	2
80.7.t	\(\chi_{80}(53, \cdot)\)	80.7.t.a	140	2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)