Properties

Label 1.16
Level 1
Weight 16
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(1))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

Trace form

\( q + 216 q^{2} - 3348 q^{3} + 13888 q^{4} + 52110 q^{5} - 723168 q^{6} + 2822456 q^{7} - 4078080 q^{8} - 3139803 q^{9} + 11255760 q^{10} + 20586852 q^{11} - 46497024 q^{12} - 190073338 q^{13} + 609650496 q^{14}+ \cdots - 64638659670156 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.16.a \(\chi_{1}(1, \cdot)\) 1.16.a.a 1 1