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Properties

Label 3.9
Level 3
Weight 9
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(3))\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\( 2 q + 90 q^{3} - 496 q^{4} + 3024 q^{6} - 3500 q^{7} - 5022 q^{9} + 10080 q^{10} - 22320 q^{12} + 51460 q^{13} - 30240 q^{15} - 135040 q^{16} + 272160 q^{18} + 37876 q^{19} - 157500 q^{21} - 312480 q^{22}+ \cdots + 84369600 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.9.b \(\chi_{3}(2, \cdot)\) 3.9.b.a 2 1