Properties

Label 107.1.b
Level 107
Weight 1
Character orbit b
Rep. character \(\chi_{107}(106,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 107 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 107.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 107 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(107, [\chi])\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\( q - q^{3} + q^{4} + O(q^{10}) \) \( q - q^{3} + q^{4} - q^{11} - q^{12} - q^{13} + q^{16} - q^{19} - q^{23} + q^{25} + q^{27} + 2q^{29} + q^{33} - q^{37} + q^{39} - q^{41} - q^{44} + 2q^{47} - q^{48} + q^{49} - q^{52} - q^{53} + q^{57} - q^{61} + q^{64} + q^{69} - q^{75} - q^{76} - q^{79} - q^{81} + 2q^{83} - 2q^{87} - q^{89} - q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(107, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
107.1.b.a \(1\) \(0.053\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-107}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots\)

Hecke characteristic polynomials

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