Properties

Label 120.1
Level 120
Weight 1
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 768
Trace bound 0

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Defining parameters

Level: \( N \) = \( 120\( 120 = 2^{3} \cdot 3 \cdot 5 \) \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(768\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(120))\).

Total New Old
Modular forms 98 14 84
Cusp forms 2 2 0
Eisenstein series 96 12 84

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

\( 2q - 2q^{4} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{6} - 2q^{9} + 2q^{10} + 2q^{15} + 2q^{16} + 2q^{24} - 2q^{25} - 4q^{31} + 2q^{36} - 2q^{40} + 2q^{49} + 2q^{54} - 2q^{60} - 2q^{64} + 4q^{79} + 2q^{81} - 2q^{90} - 2q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)

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
120.1.c \(\chi_{120}(89, \cdot)\) None 0 1
120.1.e \(\chi_{120}(31, \cdot)\) None 0 1
120.1.g \(\chi_{120}(91, \cdot)\) None 0 1
120.1.i \(\chi_{120}(29, \cdot)\) 120.1.i.a 2 1
120.1.j \(\chi_{120}(79, \cdot)\) None 0 1
120.1.l \(\chi_{120}(41, \cdot)\) None 0 1
120.1.n \(\chi_{120}(101, \cdot)\) None 0 1
120.1.p \(\chi_{120}(19, \cdot)\) None 0 1
120.1.q \(\chi_{120}(83, \cdot)\) None 0 2
120.1.t \(\chi_{120}(13, \cdot)\) None 0 2
120.1.u \(\chi_{120}(73, \cdot)\) None 0 2
120.1.x \(\chi_{120}(23, \cdot)\) None 0 2

Hecke characteristic polynomials

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