Properties

Label 71.1
Level 71
Weight 1
Dimension 3
Nonzero newspaces 1
Newforms 1
Sturm bound 420
Trace bound 0

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Defining parameters

Level: \( N \) = \( 71 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(420\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(71))\).

Total New Old
Modular forms 38 38 0
Cusp forms 3 3 0
Eisenstein series 35 35 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

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

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(71))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
71.1.b \(\chi_{71}(70, \cdot)\) 71.1.b.a 3 1
71.1.e \(\chi_{71}(14, \cdot)\) None 0 4
71.1.f \(\chi_{71}(23, \cdot)\) None 0 6
71.1.h \(\chi_{71}(7, \cdot)\) None 0 24