Space of modular forms of level 80 and weight 12

• Label: 80.12
• Level: 80
• Weight: 12
• Dimension: 1076
• Nonzero newspaces: 7
• Newform subspaces: 24
• Sturm bound: 4608
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 24 \)
Sturm bound:			\(4608\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	2168	1102	1066
Cusp forms	2056	1076	980
Eisenstein series	112	26	86

Trace form

1076 * q - 4 * q^2 - 490 * q^3 - 6168 * q^4 + 1314 * q^5 - 60720 * q^6 + 136298 * q^7 - 149680 * q^8 - 679638 * q^9 + 988940 * q^10 + 656216 * q^11 - 4600528 * q^12 - 738142 * q^13 + 3659904 * q^14 + 12476754 * q^15 + 7442880 * q^16 - 15331542 * q^17 + 64438204 * q^18 + 24391500 * q^19 - 68655172 * q^20 - 75750572 * q^21 + 170022768 * q^22 + 31878302 * q^23 + 132361880 * q^24 + 250721396 * q^25 - 611370784 * q^26 - 48682252 * q^27 + 677706184 * q^28 + 19827976 * q^29 + 227370148 * q^30 - 210241060 * q^31 - 1652007664 * q^32 - 830147456 * q^33 + 1246520528 * q^34 + 468822922 * q^35 + 28790232 * q^36 + 1036033462 * q^37 - 238453536 * q^38 + 1696880804 * q^39 - 4812403712 * q^40 + 451135896 * q^41 + 4290562232 * q^42 - 8854563298 * q^43 + 9755249928 * q^44 - 3966720956 * q^45 - 12548953384 * q^46 + 14325614266 * q^47 + 456958568 * q^48 + 18754554758 * q^49 + 14213088896 * q^50 - 25475970292 * q^51 + 373123184 * q^52 + 6776692654 * q^53 - 5868866632 * q^54 + 3648536788 * q^55 - 25821691968 * q^56 + 10336328328 * q^57 + 42982306248 * q^58 - 22708013220 * q^59 - 25649307208 * q^60 - 4675022044 * q^61 + 31629039512 * q^62 + 14936034202 * q^63 + 32098868448 * q^64 - 27541382590 * q^65 - 117112465144 * q^66 + 79827436154 * q^67 - 46935011008 * q^68 + 55339179564 * q^69 + 170652026400 * q^70 - 34247335204 * q^71 + 32505143608 * q^72 - 37283309762 * q^73 - 231302691912 * q^74 + 217989333570 * q^75 - 30017907640 * q^76 + 40925455112 * q^77 + 282892621304 * q^78 - 204600447496 * q^79 + 223363907840 * q^80 + 132740043388 * q^81 + 85864043720 * q^82 + 42653930286 * q^83 - 779621708880 * q^84 - 29803403374 * q^85 - 163075652440 * q^86 + 131238934292 * q^87 + 702083668592 * q^88 + 76346563996 * q^89 + 594798277336 * q^90 - 59039456468 * q^91 + 126476184416 * q^92 + 77277245992 * q^93 - 939406376720 * q^94 - 185800160148 * q^95 + 92862255696 * q^96 + 76550026990 * q^97 + 229011965012 * q^98 + 1341415094208 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.12.a	\(\chi_{80}(1, \cdot)\)	80.12.a.a	1	1
		80.12.a.b	1
		80.12.a.c	1
		80.12.a.d	1
		80.12.a.e	1
		80.12.a.f	1
		80.12.a.g	2
		80.12.a.h	2
		80.12.a.i	2
		80.12.a.j	2
		80.12.a.k	2
		80.12.a.l	3
		80.12.a.m	3
80.12.c	\(\chi_{80}(49, \cdot)\)	80.12.c.a	4	1
		80.12.c.b	6
		80.12.c.c	6
		80.12.c.d	16
80.12.d	\(\chi_{80}(41, \cdot)\)	None	0	1
80.12.f	\(\chi_{80}(9, \cdot)\)	None	0	1
80.12.j	\(\chi_{80}(43, \cdot)\)	80.12.j.a	260	2
80.12.l	\(\chi_{80}(21, \cdot)\)	80.12.l.a	176	2
80.12.n	\(\chi_{80}(47, \cdot)\)	80.12.n.a	2	2
		80.12.n.b	20
		80.12.n.c	44
80.12.o	\(\chi_{80}(7, \cdot)\)	None	0	2
80.12.q	\(\chi_{80}(29, \cdot)\)	80.12.q.a	260	2
80.12.s	\(\chi_{80}(3, \cdot)\)	80.12.s.a	260	2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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