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Properties

Label 13.3
Level 13
Weight 3
Dimension 8
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 42
Trace bound 2

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(13))\).

Total New Old
Modular forms 20 20 0
Cusp forms 8 8 0
Eisenstein series 12 12 0

Trace form

\( 8 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} + 4 q^{7} + 30 q^{8} + 18 q^{9} + 24 q^{10} - 18 q^{13} - 36 q^{14} - 42 q^{15} - 86 q^{16} - 12 q^{17} + 30 q^{18} + 10 q^{19} + 42 q^{20} + 72 q^{21}+ \cdots + 360 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
13.3.d \(\chi_{13}(5, \cdot)\) 13.3.d.a 4 2
13.3.f \(\chi_{13}(2, \cdot)\) 13.3.f.a 4 4