Space of modular forms of level 80 and weight 3

• Label: 80.3
• Level: 80
• Weight: 3
• Dimension: 184
• Nonzero newspaces: 7
• Newform subspaces: 11
• Sturm bound: 1152
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1152\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	440	212	228
Cusp forms	328	184	144
Eisenstein series	112	28	84

Trace form

184 * q - 4 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 + 2 * q^7 - 16 * q^8 - 18 * q^9 - 44 * q^10 + 24 * q^11 - 112 * q^12 - 2 * q^13 - 32 * q^14 + 42 * q^15 + 64 * q^16 + 66 * q^17 + 140 * q^18 - 68 * q^19 + 76 * q^20 - 12 * q^21 + 96 * q^22 - 174 * q^23 - 104 * q^24 - 36 * q^25 - 208 * q^26 - 248 * q^27 - 248 * q^28 - 176 * q^29 - 348 * q^30 - 76 * q^31 - 304 * q^32 - 220 * q^33 - 176 * q^34 + 46 * q^35 - 104 * q^36 - 42 * q^37 - 144 * q^38 + 376 * q^39 + 32 * q^40 + 24 * q^41 + 280 * q^42 + 286 * q^43 + 232 * q^44 + 268 * q^45 + 376 * q^46 + 234 * q^47 + 616 * q^48 + 458 * q^49 + 336 * q^50 - 36 * q^51 + 208 * q^52 - 90 * q^53 + 216 * q^54 - 112 * q^55 + 320 * q^56 + 80 * q^57 + 344 * q^58 - 420 * q^59 + 280 * q^60 - 68 * q^61 + 280 * q^62 - 622 * q^63 + 224 * q^64 - 218 * q^65 + 424 * q^66 - 466 * q^67 + 384 * q^68 - 256 * q^69 + 656 * q^70 - 420 * q^71 + 728 * q^72 + 18 * q^73 + 616 * q^74 - 470 * q^75 + 552 * q^76 + 268 * q^77 + 280 * q^78 - 320 * q^80 - 176 * q^81 - 824 * q^82 - 50 * q^83 - 1232 * q^84 + 446 * q^85 - 1000 * q^86 + 496 * q^87 - 784 * q^88 + 276 * q^89 - 1168 * q^90 + 956 * q^91 - 736 * q^92 + 564 * q^93 - 944 * q^94 + 1000 * q^95 - 944 * q^96 - 134 * q^97 - 876 * q^98 + 1092 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)

We only show spaces with odd 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
80.3.b	\(\chi_{80}(31, \cdot)\)	80.3.b.a	4	1
80.3.e	\(\chi_{80}(39, \cdot)\)	None	0	1
80.3.g	\(\chi_{80}(71, \cdot)\)	None	0	1
80.3.h	\(\chi_{80}(79, \cdot)\)	80.3.h.a	2	1
		80.3.h.b	4
80.3.i	\(\chi_{80}(13, \cdot)\)	80.3.i.a	44	2
80.3.k	\(\chi_{80}(19, \cdot)\)	80.3.k.a	44	2
80.3.m	\(\chi_{80}(57, \cdot)\)	None	0	2
80.3.p	\(\chi_{80}(17, \cdot)\)	80.3.p.a	2	2
		80.3.p.b	2
		80.3.p.c	2
		80.3.p.d	4
80.3.r	\(\chi_{80}(11, \cdot)\)	80.3.r.a	32	2
80.3.t	\(\chi_{80}(53, \cdot)\)	80.3.t.a	44	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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