Properties

Label 16.6
Level 16
Weight 6
Dimension 20
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(16))\).

Total New Old
Modular forms 47 25 22
Cusp forms 33 20 13
Eisenstein series 14 5 9

Trace form

\( 20 q - 2 q^{2} - 10 q^{3} - 24 q^{4} - 22 q^{5} + 112 q^{6} + 112 q^{7} + 244 q^{8} + 58 q^{9} - 436 q^{10} - 1270 q^{11} + 4 q^{12} + 58 q^{13} - 100 q^{14} + 3924 q^{15} - 872 q^{16} - 608 q^{17} - 3138 q^{18}+ \cdots - 262778 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.6.a \(\chi_{16}(1, \cdot)\) 16.6.a.a 1 1
16.6.a.b 1
16.6.b \(\chi_{16}(9, \cdot)\) None 0 1
16.6.e \(\chi_{16}(5, \cdot)\) 16.6.e.a 18 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)