Properties

Label 107.1.b
Level $107$
Weight $1$
Character orbit 107.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

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

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
107.1.b.a 107.b 107.b $1$ $0.053$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-107}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots\)