Space of modular forms of level 80 and weight 2

• Label: 80.2
• Level: 80
• Weight: 2
• Dimension: 86
• Nonzero newspaces: 7
• Newform subspaces: 13
• Sturm bound: 768
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 7 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(768\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	248	112	136
Cusp forms	137	86	51
Eisenstein series	111	26	85

Trace form

86 * q - 4 * q^2 - 2 * q^3 - 8 * q^4 - 8 * q^5 - 24 * q^6 - 6 * q^7 - 16 * q^8 - 4 * q^9 - 8 * q^10 - 16 * q^11 - 10 * q^13 - 22 * q^15 - 18 * q^17 - 12 * q^18 - 28 * q^19 - 12 * q^20 - 44 * q^21 - 8 * q^22 - 18 * q^23 - 8 * q^24 - 10 * q^25 - 24 * q^26 + 4 * q^27 + 8 * q^28 - 20 * q^29 + 28 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 + 48 * q^34 + 10 * q^35 + 56 * q^36 + 18 * q^37 + 72 * q^38 + 20 * q^39 + 80 * q^40 + 28 * q^41 + 72 * q^42 - 10 * q^43 + 56 * q^44 + 18 * q^45 + 24 * q^46 - 38 * q^47 + 40 * q^48 - 16 * q^49 + 48 * q^50 - 36 * q^51 + 32 * q^52 - 6 * q^53 + 40 * q^54 - 20 * q^55 - 40 * q^57 + 16 * q^58 - 28 * q^59 - 40 * q^60 - 40 * q^62 + 26 * q^63 - 32 * q^64 - 50 * q^65 - 88 * q^66 + 50 * q^67 - 64 * q^68 + 12 * q^69 - 88 * q^70 + 44 * q^71 - 136 * q^72 - 22 * q^73 - 96 * q^74 + 106 * q^75 - 104 * q^76 - 8 * q^77 - 136 * q^78 + 88 * q^79 - 96 * q^80 - 58 * q^81 - 72 * q^82 + 86 * q^83 - 144 * q^84 - 10 * q^85 - 80 * q^86 + 116 * q^87 - 112 * q^88 - 24 * q^89 - 124 * q^90 + 12 * q^91 - 56 * q^93 - 32 * q^94 + 52 * q^95 - 48 * q^96 - 38 * q^97 + 36 * q^98 + 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.2.a	\(\chi_{80}(1, \cdot)\)	80.2.a.a	1	1
		80.2.a.b	1
80.2.c	\(\chi_{80}(49, \cdot)\)	80.2.c.a	2	1
80.2.d	\(\chi_{80}(41, \cdot)\)	None	0	1
80.2.f	\(\chi_{80}(9, \cdot)\)	None	0	1
80.2.j	\(\chi_{80}(43, \cdot)\)	80.2.j.a	2	2
		80.2.j.b	18
80.2.l	\(\chi_{80}(21, \cdot)\)	80.2.l.a	16	2
80.2.n	\(\chi_{80}(47, \cdot)\)	80.2.n.a	2	2
		80.2.n.b	4
80.2.o	\(\chi_{80}(7, \cdot)\)	None	0	2
80.2.q	\(\chi_{80}(29, \cdot)\)	80.2.q.a	2	2
		80.2.q.b	2
		80.2.q.c	16
80.2.s	\(\chi_{80}(3, \cdot)\)	80.2.s.a	2	2
		80.2.s.b	18

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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