Properties

Label 71.1.b
Level 71
Weight 1
Character orbit b
Rep. character \(\chi_{71}(70,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(71, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
71.1.b.a \(3\) \(0.035\) \(\Q(\zeta_{14})^+\) \(D_{7}\) \(\Q(\sqrt{-71}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)