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Properties

Label 4.9
Level 4
Weight 9
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(4))\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3 q - 4 q^{2} + 144 q^{4} + 166 q^{5} - 2496 q^{6} + 11456 q^{8} - 285 q^{9} - 29064 q^{10} + 49920 q^{12} - 11418 q^{13} - 34944 q^{14} - 52992 q^{16} + 82822 q^{17} + 173436 q^{18} - 338144 q^{20} - 279552 q^{21}+ \cdots + 16078076 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.9.b \(\chi_{4}(3, \cdot)\) 4.9.b.a 1 1
4.9.b.b 2