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Properties

Label 155.1.c
Level 155
Weight 1
Character orbit c
Rep. character \(\chi_{155}(154,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 2
Sturm bound 16
Trace bound 1

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Defining parameters

Level: \( N \) = \( 155 = 5 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 155.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 155 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(155, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(155, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
155.1.c.a \(1\) \(0.077\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\)
155.1.c.b \(2\) \(0.077\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)

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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