Space of modular forms of level 80 and weight 14

• Label: 80.14
• Level: 80
• Weight: 14
• Dimension: 1274
• Nonzero newspaces: 7
• Sturm bound: 5376
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 7 \)
Sturm bound:			\(5376\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	2552	1300	1252
Cusp forms	2440	1274	1166
Eisenstein series	112	26	86

Trace form

1274 * q - 4 * q^2 + 1454 * q^3 - 728 * q^4 - 16908 * q^5 + 510096 * q^6 - 130470 * q^7 + 2153744 * q^8 - 4659936 * q^9 - 1809812 * q^10 + 24801344 * q^11 + 72933104 * q^12 - 51063490 * q^13 + 64385472 * q^14 - 172733382 * q^15 - 98108736 * q^16 + 204318390 * q^17 + 268370428 * q^18 - 1939194316 * q^19 + 337515740 * q^20 + 2022865108 * q^21 - 1494261008 * q^22 - 1926281458 * q^23 - 8031994216 * q^24 + 8256369338 * q^25 + 14224843232 * q^26 + 5164875044 * q^27 - 21093089464 * q^28 - 438429356 * q^29 + 48290289988 * q^30 + 16949654428 * q^31 - 40236329584 * q^32 + 16145842096 * q^33 + 51780120912 * q^34 - 15206235446 * q^35 - 50695475880 * q^36 - 64039725846 * q^37 - 1150313568 * q^38 + 13474174388 * q^39 + 107391504320 * q^40 - 21330758364 * q^41 - 5900972488 * q^42 + 43818832838 * q^43 - 387335584056 * q^44 + 313779813022 * q^45 + 682932822168 * q^46 - 641792494502 * q^47 - 591451828120 * q^48 + 734480783972 * q^49 - 176069043808 * q^50 + 1627302229436 * q^51 + 470043287600 * q^52 - 1274374638158 * q^53 - 263180294728 * q^54 + 361937505724 * q^55 - 754996947264 * q^56 + 596011764984 * q^57 - 1541182591160 * q^58 - 2522148408876 * q^59 + 1652106474488 * q^60 + 277302293784 * q^61 - 2819574179944 * q^62 + 889964096794 * q^63 + 1889774772448 * q^64 - 145783340506 * q^65 + 633364934984 * q^66 - 1643539876990 * q^67 + 3542051709632 * q^68 - 931936361268 * q^69 - 3048436111840 * q^70 + 7221420256652 * q^71 - 11489438723336 * q^72 - 6844698707134 * q^73 + 5695250284920 * q^74 - 12985787780646 * q^75 + 19857381586696 * q^76 + 7748860336472 * q^77 - 25469375575624 * q^78 - 9374404813928 * q^79 - 19492510671232 * q^80 + 14811511311994 * q^81 + 16481758114440 * q^82 - 11652066144954 * q^83 + 36592550874288 * q^84 - 9210664156642 * q^85 - 4408730145496 * q^86 + 19501667035892 * q^87 - 41427106068112 * q^88 - 472715753984 * q^89 + 12692976534040 * q^90 - 20475204593844 * q^91 + 45483534413024 * q^92 - 2900308255736 * q^93 - 8578786332560 * q^94 + 46949113049508 * q^95 - 2691778981296 * q^96 - 25259726192654 * q^97 - 12872128368364 * q^98 + 66637641413304 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.14.a	\(\chi_{80}(1, \cdot)\)	80.14.a.a	1	1
		80.14.a.b	1
		80.14.a.c	1
		80.14.a.d	2
		80.14.a.e	2
		80.14.a.f	3
		80.14.a.g	3
		80.14.a.h	3
		80.14.a.i	3
		80.14.a.j	3
		80.14.a.k	4
80.14.c	\(\chi_{80}(49, \cdot)\)	80.14.c.a	6	1
		80.14.c.b	6
		80.14.c.c	6
		80.14.c.d	20
80.14.d	\(\chi_{80}(41, \cdot)\)	None	0	1
80.14.f	\(\chi_{80}(9, \cdot)\)	None	0	1
80.14.j	\(\chi_{80}(43, \cdot)\)	n/a	308	2
80.14.l	\(\chi_{80}(21, \cdot)\)	n/a	208	2
80.14.n	\(\chi_{80}(47, \cdot)\)	80.14.n.a	2	2
		80.14.n.b	24
		80.14.n.c	52
80.14.o	\(\chi_{80}(7, \cdot)\)	None	0	2
80.14.q	\(\chi_{80}(29, \cdot)\)	n/a	308	2
80.14.s	\(\chi_{80}(3, \cdot)\)	n/a	308	2

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)