Properties

Label 29.6
Level 29
Weight 6
Dimension 161
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 420
Trace bound 1

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Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(420\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(29))\).

Total New Old
Modular forms 189 187 2
Cusp forms 161 161 0
Eisenstein series 28 26 2

Trace form

\( 161 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} - 14 q^{10} - 14 q^{11} - 14 q^{12} - 14 q^{13} - 14 q^{14} - 14 q^{15} - 14 q^{16} - 14 q^{17} - 14 q^{18}+ \cdots + 905996 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
29.6.a \(\chi_{29}(1, \cdot)\) 29.6.a.a 4 1
29.6.a.b 7
29.6.b \(\chi_{29}(28, \cdot)\) 29.6.b.a 12 1
29.6.d \(\chi_{29}(7, \cdot)\) 29.6.d.a 66 6
29.6.e \(\chi_{29}(4, \cdot)\) 29.6.e.a 72 6