Properties

Label 71.1.b
Level $71$
Weight $1$
Character orbit 71.b
Rep. character $\chi_{71}(70,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 71.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 71 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(71, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 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 3 0 0 0

Trace form

\( 3 q - q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + O(q^{10}) \) \( 3 q - q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 3 q^{12} - 2 q^{15} + q^{16} + 4 q^{18} - q^{19} + 4 q^{20} + 3 q^{24} + 2 q^{25} - 2 q^{27} - q^{29} + 3 q^{30} - 3 q^{32} - q^{36} - q^{37} + 5 q^{38} - 4 q^{40} - q^{43} - 3 q^{45} + 2 q^{48} + 3 q^{49} - 3 q^{50} - 4 q^{54} - 2 q^{57} - 2 q^{58} + q^{60} + 3 q^{71} + q^{72} - q^{73} + 5 q^{74} + 4 q^{75} - 3 q^{76} - q^{79} + 2 q^{80} + q^{81} - q^{83} - 2 q^{86} + 5 q^{87} - q^{89} + q^{90} - 2 q^{95} + q^{96} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(71, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
71.1.b.a 71.b 71.b $3$ $0.035$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-71}) \) None 71.1.b.a \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)