Properties

Label 80.1
Level 80
Weight 1
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 384
Trace bound 0

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Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
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

\( q - q^{5} - q^{9} + O(q^{10}) \) \( q - q^{5} - q^{9} + q^{25} + 2q^{29} - 2q^{41} + q^{45} - q^{49} - 2q^{61} + q^{81} + 2q^{89} + O(q^{100}) \)

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 the 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