Properties

Label 31.2
Level 31
Weight 2
Dimension 26
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 160
Trace bound 2

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Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(160\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(31))\).

Total New Old
Modular forms 55 55 0
Cusp forms 26 26 0
Eisenstein series 29 29 0

Trace form

\( 26 q - 12 q^{2} - 11 q^{3} - 8 q^{4} - 9 q^{5} - 3 q^{6} - 7 q^{7} - 2 q^{9} + 3 q^{10} - 3 q^{11} + 13 q^{12} - q^{13} + 9 q^{14} + 9 q^{15} + 16 q^{16} + 3 q^{17} + 24 q^{18} + 5 q^{19} + 27 q^{20} + 12 q^{21}+ \cdots + 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)

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
31.2.a \(\chi_{31}(1, \cdot)\) 31.2.a.a 2 1
31.2.c \(\chi_{31}(5, \cdot)\) 31.2.c.a 4 2
31.2.d \(\chi_{31}(2, \cdot)\) 31.2.d.a 4 4
31.2.g \(\chi_{31}(7, \cdot)\) 31.2.g.a 16 8