Properties

Label 9.3
Level 9
Weight 3
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 10 6 4
Cusp forms 2 2 0
Eisenstein series 8 4 4

Trace form

\( 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9} - 12 q^{10} - 3 q^{11} + 6 q^{12} + 4 q^{13} + 6 q^{14} + 11 q^{16} + 22 q^{19} - 6 q^{20} - 6 q^{21} + 3 q^{22} - 48 q^{23} - 45 q^{24}+ \cdots + 115 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

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
9.3.b \(\chi_{9}(8, \cdot)\) None 0 1
9.3.d \(\chi_{9}(2, \cdot)\) 9.3.d.a 2 2