Space of modular forms of level 80 and weight 10

• Label: 80.10
• Level: 80
• Weight: 10
• Dimension: 878
• Nonzero newspaces: 7
• Newform subspaces: 22
• Sturm bound: 3840
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(3840\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	1784	904	880
Cusp forms	1672	878	794
Eisenstein series	112	26	86

Trace form

878 * q - 4 * q^2 + 158 * q^3 - 344 * q^4 + 352 * q^5 + 4368 * q^6 - 2758 * q^7 + 1424 * q^8 - 11628 * q^9 - 4692 * q^10 - 109744 * q^11 - 434320 * q^12 + 258470 * q^13 + 267072 * q^14 - 586422 * q^15 + 1634496 * q^16 + 63774 * q^17 - 4359812 * q^18 - 9404 * q^19 + 3277980 * q^20 + 1863124 * q^21 + 68592 * q^22 + 53934 * q^23 - 3727720 * q^24 + 4399438 * q^25 + 12695520 * q^26 - 2152252 * q^27 - 5161912 * q^28 - 4307876 * q^29 - 28678652 * q^30 + 1005852 * q^31 + 54633616 * q^32 + 17285584 * q^33 - 53682096 * q^34 - 14276726 * q^35 - 118931880 * q^36 + 6023202 * q^37 + 117230112 * q^38 - 55844140 * q^39 + 167248960 * q^40 + 4940236 * q^41 - 340456648 * q^42 + 173446230 * q^43 - 25460920 * q^44 - 95141798 * q^45 + 24967448 * q^46 - 298361894 * q^47 + 429751400 * q^48 + 331049448 * q^49 - 126115488 * q^50 + 253264412 * q^51 - 362935120 * q^52 + 467993418 * q^53 - 130000456 * q^54 - 36232116 * q^55 - 53022528 * q^56 - 176735592 * q^57 + 356543560 * q^58 - 176837116 * q^59 - 231131272 * q^60 + 110282384 * q^61 + 273577880 * q^62 + 511442458 * q^63 + 764733664 * q^64 + 447916894 * q^65 + 573711560 * q^66 + 535990418 * q^67 - 969283648 * q^68 - 1007670132 * q^69 - 1401948640 * q^70 - 1090988692 * q^71 + 977392504 * q^72 + 713861754 * q^73 + 2188462584 * q^74 - 1303824246 * q^75 + 875120008 * q^76 + 25935928 * q^77 - 1448704456 * q^78 + 750500312 * q^79 - 2174562432 * q^80 + 1375360318 * q^81 + 1080832776 * q^82 + 928974710 * q^83 + 3673592496 * q^84 - 2162681882 * q^85 + 3074251816 * q^86 - 4838564236 * q^87 - 2311113872 * q^88 - 1605217032 * q^89 - 10365321320 * q^90 + 2129646988 * q^91 - 144567840 * q^92 + 3624143176 * q^93 + 4867285360 * q^94 + 1612367188 * q^95 + 18717655632 * q^96 - 787562518 * q^97 + 2236117908 * q^98 - 11854403736 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.10.a	\(\chi_{80}(1, \cdot)\)	80.10.a.a	1	1
		80.10.a.b	1
		80.10.a.c	1
		80.10.a.d	1
		80.10.a.e	1
		80.10.a.f	2
		80.10.a.g	2
		80.10.a.h	2
		80.10.a.i	2
		80.10.a.j	2
		80.10.a.k	3
80.10.c	\(\chi_{80}(49, \cdot)\)	80.10.c.a	4	1
		80.10.c.b	4
		80.10.c.c	4
		80.10.c.d	14
80.10.d	\(\chi_{80}(41, \cdot)\)	None	0	1
80.10.f	\(\chi_{80}(9, \cdot)\)	None	0	1
80.10.j	\(\chi_{80}(43, \cdot)\)	80.10.j.a	212	2
80.10.l	\(\chi_{80}(21, \cdot)\)	80.10.l.a	144	2
80.10.n	\(\chi_{80}(47, \cdot)\)	80.10.n.a	2	2
		80.10.n.b	16
		80.10.n.c	36
80.10.o	\(\chi_{80}(7, \cdot)\)	None	0	2
80.10.q	\(\chi_{80}(29, \cdot)\)	80.10.q.a	212	2
80.10.s	\(\chi_{80}(3, \cdot)\)	80.10.s.a	212	2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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