Properties

Label 160.1
Level 160
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 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: \( 1 \)
Newform subspaces: \( 1 \)
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

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

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( \)
$3$ \( 1 + T^{4} \)
$5$ \( 1 + T^{2} \)
$7$ \( 1 + T^{4} \)
$11$ \( ( 1 + T^{2} )^{2} \)
$13$ \( ( 1 + T )^{2}( 1 + T^{2} ) \)
$17$ \( ( 1 + T )^{2}( 1 + T^{2} ) \)
$19$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$23$ \( 1 + T^{4} \)
$29$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$31$ \( ( 1 + T^{2} )^{2} \)
$37$ \( ( 1 - T )^{2}( 1 + T^{2} ) \)
$41$ \( ( 1 + T^{2} )^{2} \)
$43$ \( 1 + T^{4} \)
$47$ \( 1 + T^{4} \)
$53$ \( ( 1 - T )^{2}( 1 + T^{2} ) \)
$59$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$61$ \( ( 1 + T^{2} )^{2} \)
$67$ \( 1 + T^{4} \)
$71$ \( ( 1 + T^{2} )^{2} \)
$73$ \( ( 1 - T )^{2}( 1 + T^{2} ) \)
$79$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$83$ \( 1 + T^{4} \)
$89$ \( ( 1 - T )^{2}( 1 + T )^{2} \)
$97$ \( ( 1 - T )^{2}( 1 + T^{2} ) \)
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