Space of modular forms of level 80 and weight 22

• Label: 80.22
• Level: 80
• Weight: 22
• Dimension: 2066
• Nonzero newspaces: 7
• Sturm bound: 8448
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 22 \)
Nonzero newspaces:			\( 7 \)
Sturm bound:			\(8448\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	4088	2092	1996
Cusp forms	3976	2066	1910
Eisenstein series	112	26	86

Trace form

2066 * q - 4 * q^2 + 118094 * q^3 - 3208664 * q^4 + 10391772 * q^5 + 285521808 * q^6 + 572793242 * q^7 + 10875501584 * q^8 - 72487634760 * q^9 + 101897120748 * q^10 - 46375414624 * q^11 - 733022876176 * q^12 + 322965790190 * q^13 - 7580685132096 * q^14 - 7349759520102 * q^15 - 2494015836480 * q^16 - 3263572335642 * q^17 - 49453996526852 * q^18 + 147333910203028 * q^19 + 3577794932060 * q^20 + 37926547941076 * q^21 + 550108779528432 * q^22 - 161368512043570 * q^23 + 1136300970032792 * q^24 + 3699230469963538 * q^25 - 5479412931410464 * q^26 + 499347419493860 * q^27 + 10964652877800776 * q^28 + 675350950905028 * q^29 + 4597200737916868 * q^30 + 16688019010815132 * q^31 - 35947710854940784 * q^32 + 29152106426854768 * q^33 - 80000536638278832 * q^34 + 23117617127690314 * q^35 - 2557502953387176 * q^36 - 131274141198019590 * q^37 + 103751127907384992 * q^38 + 252460356768702068 * q^39 + 46869668737627840 * q^40 - 321132812496539436 * q^41 - 774242743170591688 * q^42 - 285816113746476762 * q^43 - 511672260626930232 * q^44 - 1346095345468240538 * q^45 + 1642694906299211672 * q^46 - 1971518479379273126 * q^47 - 1973931489747707800 * q^48 + 9622498487102800476 * q^49 + 5124296838569464352 * q^50 - 7401439186394506756 * q^51 + 8076683437849466672 * q^52 - 1892790250424233982 * q^53 - 4774205944404623944 * q^54 - 4169115481482375396 * q^55 - 1939695110050020672 * q^56 + 8889431709112869816 * q^57 + 26415266315164075336 * q^58 - 28985839975825596684 * q^59 - 19454776049293193992 * q^60 - 14162903220944081752 * q^61 + 462156871721359256 * q^62 + 43230733385957501722 * q^63 - 15695702234499788576 * q^64 - 1775653328256031306 * q^65 - 133369744855066969528 * q^66 - 5577204509229346078 * q^67 + 144679867937795324096 * q^68 + 65573110686986684748 * q^69 - 231285349724182006240 * q^70 - 185234387215497176884 * q^71 + 333335081768350597624 * q^72 + 39297009517227897810 * q^73 - 157838855327295221640 * q^74 - 116428412488768093446 * q^75 - 41839419878608975352 * q^76 - 16137063575875965544 * q^77 - 510068269386457038664 * q^78 + 510132072927137745176 * q^79 - 202549109186782786432 * q^80 + 781740194756710147570 * q^81 - 615273121238004407928 * q^82 - 305344160183424034458 * q^83 + 1018003235583550185648 * q^84 - 135203167097661419762 * q^85 - 2076348202158725300440 * q^86 - 2970057196825353167116 * q^87 - 1421286961516590852752 * q^88 - 12000872524841994992 * q^89 - 384477461723338744040 * q^90 + 258703845262081497292 * q^91 - 3174328638353823628576 * q^92 - 2382244325253657379448 * q^93 - 2285361209442272186768 * q^94 + 3183596806088816260548 * q^95 + 11518115486707388691024 * q^96 + 284245829280769511426 * q^97 - 13054850946853380350956 * q^98 - 5811747424072950727464 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.22.a	\(\chi_{80}(1, \cdot)\)	80.22.a.a	1	1
		80.22.a.b	2
		80.22.a.c	2
		80.22.a.d	2
		80.22.a.e	3
		80.22.a.f	3
		80.22.a.g	4
		80.22.a.h	4
		80.22.a.i	5
		80.22.a.j	5
		80.22.a.k	5
		80.22.a.l	6
80.22.c	\(\chi_{80}(49, \cdot)\)	80.22.c.a	10	1
		80.22.c.b	10
		80.22.c.c	10
		80.22.c.d	32
80.22.d	\(\chi_{80}(41, \cdot)\)	None	0	1
80.22.f	\(\chi_{80}(9, \cdot)\)	None	0	1
80.22.j	\(\chi_{80}(43, \cdot)\)	n/a	500	2
80.22.l	\(\chi_{80}(21, \cdot)\)	n/a	336	2
80.22.n	\(\chi_{80}(47, \cdot)\)	n/a	126	2
80.22.o	\(\chi_{80}(7, \cdot)\)	None	0	2
80.22.q	\(\chi_{80}(29, \cdot)\)	n/a	500	2
80.22.s	\(\chi_{80}(3, \cdot)\)	n/a	500	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)