Space of modular forms of level 80 and weight 1

• Label: 80.1
• Level: 80
• Weight: 1
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 384
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(80))\).

	Total	New	Old
Modular forms	57	15	42
Cusp forms	1	1	0
Eisenstein series	56	14	42

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q - q^{5} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.1.b	\(\chi_{80}(31, \cdot)\)	None	0	1
80.1.e	\(\chi_{80}(39, \cdot)\)	None	0	1
80.1.g	\(\chi_{80}(71, \cdot)\)	None	0	1
80.1.h	\(\chi_{80}(79, \cdot)\)	80.1.h.a	1	1
80.1.i	\(\chi_{80}(13, \cdot)\)	None	0	2
80.1.k	\(\chi_{80}(19, \cdot)\)	None	0	2
80.1.m	\(\chi_{80}(57, \cdot)\)	None	0	2
80.1.p	\(\chi_{80}(17, \cdot)\)	None	0	2
80.1.r	\(\chi_{80}(11, \cdot)\)	None	0	2
80.1.t	\(\chi_{80}(53, \cdot)\)	None	0	2