Properties

Label 16.2
Level 16
Weight 2
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 32
Trace bound 0

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(16))\).

Total New Old
Modular forms 15 7 8
Cusp forms 2 2 0
Eisenstein series 13 5 8

Trace form

\( 2 q - 2 q^{2} - 2 q^{3} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 2 q^{11} - 4 q^{12} - 2 q^{13} - 4 q^{14} + 4 q^{15} - 8 q^{16} - 4 q^{17} + 2 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{26} - 8 q^{27} + 8 q^{28}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.2.a \(\chi_{16}(1, \cdot)\) None 0 1
16.2.b \(\chi_{16}(9, \cdot)\) None 0 1
16.2.e \(\chi_{16}(5, \cdot)\) 16.2.e.a 2 2