Properties

Label 47.1.b
Level $47$
Weight $1$
Character orbit 47.b
Rep. character $\chi_{47}(46,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 47.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 47 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(47, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 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 2 0 0 0

Trace form

\( 2 q - q^{2} - q^{3} + q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + q^{9} + O(q^{10}) \) \( 2 q - q^{2} - q^{3} + q^{4} - 2 q^{6} - q^{7} - 2 q^{8} + q^{9} + 2 q^{12} + 3 q^{14} - q^{17} + 2 q^{18} - 2 q^{21} + q^{24} + 2 q^{25} - 2 q^{27} - 3 q^{28} + 2 q^{32} - 2 q^{34} - 2 q^{36} - q^{37} + q^{42} + 2 q^{47} + q^{49} - q^{50} + 3 q^{51} - q^{53} + q^{54} + q^{56} - q^{59} - q^{61} + 2 q^{63} - q^{64} + 2 q^{68} - q^{71} - q^{72} - 2 q^{74} - q^{75} - q^{79} + 4 q^{83} - q^{84} - q^{89} - q^{94} - q^{96} - q^{97} - 3 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(47, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
47.1.b.a 47.b 47.b $2$ $0.023$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-47}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)