Space of modular forms of level 80 and weight 6

• Label: 80.6
• Level: 80
• Weight: 6
• Dimension: 482
• Nonzero newspaces: 7
• Newform subspaces: 21
• Sturm bound: 2304
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(2304\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	1016	508	508
Cusp forms	904	482	422
Eisenstein series	112	26	86

Trace form

482 * q - 4 * q^2 + 14 * q^3 + 40 * q^4 + 12 * q^5 - 240 * q^6 - 230 * q^7 - 496 * q^8 - 120 * q^9 + 428 * q^10 + 2528 * q^11 - 16 * q^12 - 370 * q^13 + 192 * q^14 - 1062 * q^15 + 1728 * q^16 + 390 * q^17 + 6268 * q^18 + 8148 * q^19 - 2980 * q^20 - 5420 * q^21 - 8848 * q^22 - 4018 * q^23 - 16744 * q^24 + 10338 * q^25 - 14752 * q^26 + 1124 * q^27 + 22856 * q^28 + 8164 * q^29 + 35908 * q^30 + 12956 * q^31 - 3184 * q^32 - 30224 * q^33 - 45744 * q^34 - 14006 * q^35 + 12120 * q^36 + 38874 * q^37 - 31968 * q^38 + 53492 * q^39 + 43200 * q^40 + 21876 * q^41 - 9928 * q^42 - 11162 * q^43 + 38856 * q^44 - 56618 * q^45 + 41368 * q^46 - 107942 * q^47 + 116840 * q^48 + 42604 * q^49 + 38432 * q^50 + 28028 * q^51 - 26320 * q^52 + 7522 * q^53 - 355144 * q^54 + 10844 * q^55 - 382272 * q^56 - 184776 * q^57 - 213560 * q^58 - 47436 * q^59 + 146168 * q^60 + 154504 * q^61 + 547736 * q^62 + 159514 * q^63 + 291040 * q^64 + 95894 * q^65 + 341576 * q^66 + 42530 * q^67 + 36032 * q^68 - 151476 * q^69 - 12640 * q^70 - 399796 * q^71 - 580616 * q^72 - 133454 * q^73 - 342792 * q^74 + 20154 * q^75 - 68600 * q^76 + 105752 * q^77 + 374456 * q^78 + 665112 * q^79 + 61568 * q^80 + 193282 * q^81 - 180600 * q^82 + 26406 * q^83 - 591696 * q^84 + 88878 * q^85 - 758872 * q^86 - 599308 * q^87 - 557712 * q^88 - 27920 * q^89 + 911320 * q^90 - 66100 * q^91 + 1144544 * q^92 - 210296 * q^93 + 1145200 * q^94 + 59268 * q^95 + 586320 * q^96 - 36894 * q^97 + 212756 * q^98 + 881304 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.6.a	\(\chi_{80}(1, \cdot)\)	80.6.a.a	1	1
		80.6.a.b	1
		80.6.a.c	1
		80.6.a.d	1
		80.6.a.e	1
		80.6.a.f	1
		80.6.a.g	1
		80.6.a.h	1
		80.6.a.i	2
80.6.c	\(\chi_{80}(49, \cdot)\)	80.6.c.a	2	1
		80.6.c.b	2
		80.6.c.c	2
		80.6.c.d	8
80.6.d	\(\chi_{80}(41, \cdot)\)	None	0	1
80.6.f	\(\chi_{80}(9, \cdot)\)	None	0	1
80.6.j	\(\chi_{80}(43, \cdot)\)	80.6.j.a	116	2
80.6.l	\(\chi_{80}(21, \cdot)\)	80.6.l.a	80	2
80.6.n	\(\chi_{80}(47, \cdot)\)	80.6.n.a	2	2
		80.6.n.b	4
		80.6.n.c	4
		80.6.n.d	20
80.6.o	\(\chi_{80}(7, \cdot)\)	None	0	2
80.6.q	\(\chi_{80}(29, \cdot)\)	80.6.q.a	116	2
80.6.s	\(\chi_{80}(3, \cdot)\)	80.6.s.a	116	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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