Properties

Label 58.2
Level 58
Weight 2
Dimension 34
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 420
Trace bound 3

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Defining parameters

Level: \( N \) = \( 58 = 2 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(420\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(58))\).

Total New Old
Modular forms 133 34 99
Cusp forms 78 34 44
Eisenstein series 55 0 55

Trace form

\( 34 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 6 q^{10} - 12 q^{11} - 4 q^{12} - 14 q^{13} - 8 q^{14} - 24 q^{15} - q^{16} - 18 q^{17} - 13 q^{18} - 20 q^{19} + q^{20}+ \cdots + 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)

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
58.2.a \(\chi_{58}(1, \cdot)\) 58.2.a.a 1 1
58.2.a.b 1
58.2.b \(\chi_{58}(57, \cdot)\) 58.2.b.a 2 1
58.2.d \(\chi_{58}(7, \cdot)\) 58.2.d.a 6 6
58.2.d.b 12
58.2.e \(\chi_{58}(5, \cdot)\) 58.2.e.a 12 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(58))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(58)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)