Properties

Label 160.1
Level 160
Weight 1
Dimension 2
Nonzero newspaces 1
Newforms 1
Sturm bound 1536
Trace bound 0

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Defining parameters

Level: \( N \) = \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(1536\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(160))\).

Total New Old
Modular forms 132 32 100
Cusp forms 4 2 2
Eisenstein series 128 30 98

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\(2q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.1.b \(\chi_{160}(31, \cdot)\) None 0 1
160.1.e \(\chi_{160}(79, \cdot)\) None 0 1
160.1.g \(\chi_{160}(111, \cdot)\) None 0 1
160.1.h \(\chi_{160}(159, \cdot)\) None 0 1
160.1.i \(\chi_{160}(57, \cdot)\) None 0 2
160.1.k \(\chi_{160}(39, \cdot)\) None 0 2
160.1.m \(\chi_{160}(17, \cdot)\) None 0 2
160.1.p \(\chi_{160}(33, \cdot)\) 160.1.p.a 2 2
160.1.r \(\chi_{160}(71, \cdot)\) None 0 2
160.1.t \(\chi_{160}(137, \cdot)\) None 0 2
160.1.v \(\chi_{160}(13, \cdot)\) None 0 4
160.1.w \(\chi_{160}(11, \cdot)\) None 0 4
160.1.y \(\chi_{160}(19, \cdot)\) None 0 4
160.1.bb \(\chi_{160}(53, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(160)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)