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Properties

Label 31.4
Level 31
Weight 4
Dimension 105
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(31))\).

Total New Old
Modular forms 135 133 2
Cusp forms 105 105 0
Eisenstein series 30 28 2

Trace form

\( 105 q - 15 q^{2} - 15 q^{3} - 15 q^{4} - 15 q^{5} - 15 q^{6} - 15 q^{7} - 15 q^{8} - 15 q^{9} - 15 q^{10} - 15 q^{11} - 15 q^{12} - 15 q^{13} - 15 q^{14} - 15 q^{15} - 15 q^{16} - 15 q^{17} - 15 q^{18}+ \cdots + 3735 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(31))\)

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
31.4.a \(\chi_{31}(1, \cdot)\) 31.4.a.a 2 1
31.4.a.b 5
31.4.c \(\chi_{31}(5, \cdot)\) 31.4.c.a 14 2
31.4.d \(\chi_{31}(2, \cdot)\) 31.4.d.a 28 4
31.4.g \(\chi_{31}(7, \cdot)\) 31.4.g.a 56 8