Properties

Label 155.1
Level 155
Weight 1
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 1920
Trace bound 0

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Defining parameters

Level: \( N \) = \( 155 = 5 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(1920\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(155))\).

Total New Old
Modular forms 125 89 36
Cusp forms 5 3 2
Eisenstein series 120 86 34

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3q - 3q^{4} - 3q^{9} + O(q^{10}) \) \( 3q - 3q^{4} - 3q^{9} - 3q^{10} + 6q^{14} + 3q^{16} - 3q^{20} - 3q^{31} + 3q^{35} + 3q^{36} + 3q^{40} - 3q^{49} - 3q^{50} - 6q^{56} + 3q^{64} + 3q^{70} - 6q^{76} + 3q^{81} + 3q^{90} + 3q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(155))\)

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
155.1.c \(\chi_{155}(154, \cdot)\) 155.1.c.a 1 1
155.1.c.b 2
155.1.d \(\chi_{155}(61, \cdot)\) None 0 1
155.1.g \(\chi_{155}(32, \cdot)\) None 0 2
155.1.i \(\chi_{155}(99, \cdot)\) None 0 2
155.1.k \(\chi_{155}(6, \cdot)\) None 0 2
155.1.l \(\chi_{155}(46, \cdot)\) None 0 4
155.1.m \(\chi_{155}(29, \cdot)\) None 0 4
155.1.o \(\chi_{155}(67, \cdot)\) None 0 4
155.1.s \(\chi_{155}(2, \cdot)\) None 0 8
155.1.t \(\chi_{155}(11, \cdot)\) None 0 8
155.1.v \(\chi_{155}(24, \cdot)\) None 0 8
155.1.w \(\chi_{155}(7, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(155))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(155)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

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